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If the least common multiple of m and n is 24, then what is

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shahul
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If the least common multiple of m and n is 24, then what is [#permalink] New post   30 May 2018, 01:22
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If the least common multiple of m and n is 24, then what is the first integer larger than 3070 that is divisible by both m and n?

(A) 3072

(B) 3078

(C) 3084

(D) 3088

(E) 3094
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A
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sandy
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Re: If the least common multiple of m and n is 24, then what is [#permalink] New post   05 Jun 2018, 13:10
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Least common multiple of \(m\) and \(n\) is 24.

So for a number larger than 3070 to be divisible by both \(m\) and \(n\), it must be divisible by the least common multiple of m and n as well.

Using the gre calculator \(\frac{3070}{24}=127.9166\).

Clearly multiple of 24 larger than 3070 is \(128 \times 24=3072\).
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Re: If the least common multiple of m and n is 24, then what is [#permalink] New post   08 Jun 2018, 09:26
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24=23∗324=23∗3

As per divisibility rule -

1. For a number to be divisible by 8, the last 3 digits must be divisible by 8.
2. For a number to be divisible by 3, the sum of the digits must be divisible by 3.

Check the options only (A) follows

1. 072 - Divisible by 8
2. 3072 - Sum of the digits is 12 , which is divisible by 3
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Re: If the least common multiple of m and n is 24, then what is [#permalink] New post   27 Oct 2022, 10:03
Given that LCM of m and n is 24 and we need to find what is the first integer larger than 3070 that is divisible by both m and n

LCM(m,n) = 24 => Both m and n are multiples of 24

=> For a number to be divisible by m and n it should be divisible by 24 for sure.

Number greater than 3070 which is divisible by 24 is 3072 (as 072 is divisible by 8 and 3072 is divisible by 3)

Watch this video to learn about Divisibility Rules

So , Answer will be A
Hope it helps!

To learn more about LCM and GCD watch the following videos



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Re: If the least common multiple of m and n is 24, then what is [#permalink]
27 Oct 2022, 10:03
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