LCD and GCF Help

[lightning09]

Hello I need some help with finding out how to find the GCF and LCM.

Ex: What is the LCM of 3, and 9. What is the GCF of 10 and 100.

Thanks!

 

[Deleted member 4993]

Hello I need some help with finding out how to find the GCF and LCM.

Ex: What is the LCM of 3, and 9. What is the GCF of 10 and 100.

Thanks!

For a quick review go to:

http://www.purplemath.com/modules/lcm_gcf.htm

Then:

Please read the post titled "Read before Posting".

We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")

Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[HallsofIvy]

Hello I need some help with finding out how to find the GCF and LCM.

Ex: What is the LCM of 3, and 9. What is the GCF of 10 and 100.

Thanks!

Do you understand what "LCM" and "GCF" mean?
"LCM= Least Common Multiple"- the smallest integer that is a multiple of both.
The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, .... The multiples of 9 are 9, 18, 27, 36, .... What is the smallest number that is on both lists?

The multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, .... The multiples of 100 are 200, 300, 400, 500, .... What is the smallest number that is on both lists?

"GCF= Greatest Common Factor"- the largest integer that divides both.
The factors of 1 are 1 and 3. The factors of 9 are 1, 3, and 9. What is largest number that is on both lists?

The factors of 10 are 1, 2, 5, and 10. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. What is the largest number that is on both lists?

(These particular problems are especially easy because in both the second number is a multiple of the first. The LCM of a and ba (for any integer a and b) is ba and the GCF is a.)

 

[JeffM]

Do you understand what "LCM" and "GCF" mean?
"LCM= Least Common Multiple"- the smallest integer that is a multiple of both.
The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, .... The multiples of 9 are 9, 18, 27, 36, .... What is the smallest number that is on both lists?

The multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, .... The multiples of 100 are 100, 200, 300, 400, 500, .... What is the smallest number that is on both lists?

"GCF= Greatest Common Factor"- the largest integer that divides both.
The factors of 1 are 1 and 3. The factors of 9 are 1, 3, and 9. What is largest number that is on both lists?

The factors of 10 are 1, 2, 5, and 10. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. What is the largest number that is on both lists?

(These particular problems are especially easy because in both the second number is a multiple of the first. The LCM of a and ba (for any integer a and b) is ba and the GCF is a.)

What I dislike about this problem is that the answers do not reflect the typical use of the concepts being taught. When I must add 1/10 and 1/100, I do not say to myself what is the least common multiple so I can adjust both denominators to get a common denominator. I say 100 is an integer multiple of 10, and I adjust just one denominator. In other words, the first step is to ask whether the denominator with the greater magnitude is an integer multiple of the denominator with a smaller magnitude. Least common multiple as a practical tool only arises when the answer to that question is negative. (Of course I seldom bother with least common multiple at all; I just multiply the two denominators.)

Similarly when simplifying the fraction 3/9, I do not first say to myself, what is the greatest common factor. 3 obviously divides evenly into 9 so
3/9 = 1/3 without any further fuss. Greatest common factor comes in when the numbers are too large to do division by pure recognition or when the numbers do not divide evenly. 42/63. Now seeing that 21 is the largest common factor leads to (21 * 2)/(21 * 3) = 2/3.

The fact that Halls forgot to write down 100 as a multiple of 100 is proof that this problem is trying to play a psychological trick on a child. It makes me angry.

 

[lightning09]

Reply:

For a quick review go to:

http://www.purplemath.com/modules/lcm_gcf.htm

Then:

Please read the post titled "Read before Posting".

We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")

Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.

Work:
LCD:

3:1,3

9:3,3

LCD:3

GCF:

10:2,5

100:2,2,5,5

GCF:50

If they are right please give me another problem.

If they are wrong please explain.

 

[lightning09]

Reply:

Do you understand what "LCM" and "GCF" mean?
"LCM= Least Common Multiple"- the smallest integer that is a multiple of both.
The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, .... The multiples of 9 are 9, 18, 27, 36, .... What is the smallest number that is on both lists?

The multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, .... The multiples of 100 are 200, 300, 400, 500, .... What is the smallest number that is on both lists?

"GCF= Greatest Common Factor"- the largest integer that divides both.
The factors of 1 are 1 and 3. The factors of 9 are 1, 3, and 9. What is largest number that is on both lists?

The factors of 10 are 1, 2, 5, and 10. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. What is the largest number that is on both lists?

(These particular problems are especially easy because in both the second number is a multiple of the first. The LCM of a and ba (for any integer a and b) is ba and the GCF is a.)

This is not what I need help with. Example is above this post.

 

[lightning09]

Reply:

What I dislike about this problem is that the answers do not reflect the typical use of the concepts being taught. When I must add 1/10 and 1/100, I do not say to myself what is the least common multiple so I can adjust both denominators to get a common denominator. I say 100 is an integer multiple of 10, and I adjust just one denominator. In other words, the first step is to ask whether the denominator with the greater magnitude is an integer multiple of the denominator with a smaller magnitude. Least common multiple as a practical tool only arises when the answer to that question is negative. (Of course I seldom bother with least common multiple at all; I just multiply the two denominators.)

Similarly when simplifying the fraction 3/9, I do not first say to myself, what is the greatest common factor. 3 obviously divides evenly into 9 so
3/9 = 1/3 without any further fuss. Greatest common factor comes in when the numbers are too large to do division by pure recognition or when the numbers do not divide evenly. 42/63. Now seeing that 21 is the largest common factor leads to (21 * 2)/(21 * 3) = 2/3.

The fact that Halls forgot to write down 100 as a multiple of 100 is proof that this problem is trying to play a psychological trick on a child. It makes me angry.

I don't think this is the right problem either. Example is 2 posts above this post.

 

[JeffM]

Work:
LCD: Original problem asked for least common multiple or LCM. What is LCD?

3:1,3 Purple math method asks for prime factors. 1 is not considered a prime number. So picky answer would be 3.

9:3,3 Correct prime factors

LCD:3 The LCM = 3 * 3 = 9.

GCF:

10:2,5 Correct prime factors

100:2,2,5,5 Correct prime factors

GCF:50 Incorrect GCF = 2 * 5 = 10

If they are right please give me another problem.

If they are wrong please explain.

Reread purplemath, then try this. Find the least common multiple and greatest common factor of 68 and 102.

 

[lightning09]

Reply:

Reread purplemath, then try this. Find the least common multiple and greatest common factor of 68 and 102.

102:2,3,17

68:2,2,17

GCF:34

LCM:68

I got this. I am a litttle confused.

 

[Deleted member 4993]

102:2,3,17

68:2,2,17

GCF:34

LCM:68

I got this. I am a litttle confused.

Your GCF is correct.

However, you must remember that the lowest common multiple is greater than or equal to the largest number of the given set.

So LCM of must be equal to or greater than 102 (for the problem at hand.

The LCM = 17 * 2 * 2 * 3 ............ It must include all the prime factors with largest exponent for each factor.

LCM = 204

 

[mmm4444bot]

GCF:

10:2,5

100:2,2,5,5

GCF:50

50 is clearly not a factor of 10. :?

Did you forget that you were looking for a factor of both 100 and 10?

 

[JeffM]

102:2,3,17

68:2,2,17

GCF:34

LCM:68

I got this. I am a litttle confused.

Halls of Ivy asked you what the definitions of these terms were. It is very important to UNDERSTAND definitions, not just memorize them.

A FACTOR of a is a number that divides evenly into a. So a factor of a is NOT LARGER than a. With me so far?

A PRIME is a number that has exactly TWO distinct factors, 1 and itself. Notice that 1 is consequently not prime.

A COMMON factor of a and b is a factor of BOTH a and b, one that they share in common. So it divides evenly into both a and b and is NOT LARGER than the smaller of a and b. Makes sense, right?

Every number larger than 1 has AT LEAST two distinct factors but MAY have more than two. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30. So a and b may have more than one common factor. Factors of 15: 1, 3, 5, 15. Common factors of 15 and 30: 1, 3, 5, 15. Got that concept?

So, putting these definitions together, the GREATEST common factor of a and b is the LARGEST number that divides evenly into both a and b. It is just a matter of understanding what the words mean.

A MULTIPLE of a is a number that a divides into evenly. In other words, a is a factor of a multiple of a. So a multiple of a is NOT SMALLER than a. Not hard to understand.

A COMMON multiple of a and b is a number that BOTH a and b divide into evenly. Consequently, it is NOT SMALLER than the larger of a and b. Not that hard to grasp, is it?

Example: 6 and 14 divide evenly into 42, 84, 420, 12,600, and so on forever.

So, putting these definitions together, the LEAST common factor of a and b is the SMALLEST number that a and b both divide into evenly. It is just a matter of understanding what the words mean.

Purplemath tells you how to find greatest common factors and least common multiples in a systematic way, but a system helps only if you understand what the system is helping you to do. Halls of Ivy gave you good advice

Clearer now?

 

[mmm4444bot]

I wish "they'd" settle on ONE … form

LCM and GCD are used [in UBasic]

So, you prefer the instruction to "find all divisors of the polynomial" over "find all factors of the polynomial".

A factor is a divisor, and a divisor is a factor. Why does everything need to be called Jack? :?

< heh, heh, heh >

 

[lightning09]

Reply:

Your GCF is correct.

However, you must remember that the lowest common multiple is greater than or equal to the largest number of the given set.

So LCM of must be equal to or greater than 102 (for the problem at hand.

The LCM = 17 * 2 * 2 * 3 ............ It must include all the prime factors with largest exponent for each factor.

LCM = 204

That answer makes a lot more sense.

 

[lightning09]

Reply:

Halls of Ivy asked you what the definitions of these terms were. It is very important to UNDERSTAND definitions, not just memorize them.

A FACTOR of a is a number that divides evenly into a. So a factor of a is NOT LARGER than a. With me so far?

A PRIME is a number that has exactly TWO distinct factors, 1 and itself. Notice that 1 is consequently not prime.

A COMMON factor of a and b is a factor of BOTH a and b, one that they share in common. So it divides evenly into both a and b and is NOT LARGER than the smaller of a and b. Makes sense, right?

Every number larger than 1 has AT LEAST two distinct factors but MAY have more than two. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30. So a and b may have more than one common factor. Factors of 15: 1, 3, 5, 15. Common factors of 15 and 30: 1, 3, 5, 15. Got that concept?

So, putting these definitions together, the GREATEST common factor of a and b is the LARGEST number that divides evenly into both a and b. It is just a matter of understanding what the words mean.

A MULTIPLE of a is a number that a divides into evenly. In other words, a is a factor of a multiple of a. So a multiple of a is NOT SMALLER than a. Not hard to understand.

A COMMON multiple of a and b is a number that BOTH a and b divide into evenly. Consequently, it is NOT SMALLER than the larger of a and b. Not that hard to grasp, is it?

Example: 6 and 14 divide evenly into 42, 84, 420, 12,600, and so on forever.

So, putting these definitions together, the LEAST common factor of a and b is the SMALLEST number that a and b both divide into evenly. It is just a matter of understanding what the words mean.

Purplemath tells you how to find greatest common factors and least common multiples in a systematic way, but a system helps only if you understand what the system is helping you to do. Halls of Ivy gave you good advice

Clearer now?

Yeah its clearer now.