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# Answer Choices- 127, 254, 16,383, and 32,766

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320
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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

#1
+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
+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.

Guest Jan 12, 2019
edited by Guest  Jan 12, 2019
#2
+109512
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Great explanation guest. !

Melody  Jan 12, 2019
#3
+111321
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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....!!!!

CPhill  Jan 12, 2019