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If the least common multiple of the first 130 positive integers is divided by the least common multiple of the first 125 positive integers, the quotient is?

 
 Jan 11, 2019

Best Answer 

 #1
avatar
+2

The LCM of all numbers from 1 to 130 is the PRODUCT of all Prime numbers up 130. That is:

2 x 3 x  5 x 7...........up to 127.

 

The LCM of all numbers from 1 to 125 is exactly the same EXCEPT 127, since it is > 125.

 

Therefore, when you divide them everything cancels out EXCEPT 127, which is the QUOTIENT.

 
 Jan 12, 2019
edited by Guest  Jan 12, 2019
 #1
avatar
+2
Best Answer

The LCM of all numbers from 1 to 130 is the PRODUCT of all Prime numbers up 130. That is:

2 x 3 x  5 x 7...........up to 127.

 

The LCM of all numbers from 1 to 125 is exactly the same EXCEPT 127, since it is > 125.

 

Therefore, when you divide them everything cancels out EXCEPT 127, which is the QUOTIENT.

 
Guest Jan 12, 2019
edited by Guest  Jan 12, 2019
 #2
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+2

Great explanation guest. !

 
Melody  Jan 12, 2019
 #3
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Agree with Melody.....I never noticed that the LCM of the first n positive integers is just the product of all the primes from 2 to n....!!!!

 

 

cool cool cool

 
CPhill  Jan 12, 2019

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