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

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If the least common multiple of m and n is 24, then what is [#permalink] New post 21 Apr 2018, 05:02
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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
[Reveal] Spoiler: OA

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Re: If the least common multiple of m and n is 24, then what is [#permalink] New post 24 Apr 2018, 01:59
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Since \(24\) is the least common multiple of \(m\) and \(n\), all the values divisible by \(m\) and \(n\) is also divisible by \(24\)
We are asked to find the first integer greater than \(3070\) i.e divisible by \(m\) and \(n.\) This means we have to find the first
integer greater than \(3070\) which is divisible by \(24\).
\(\frac{3070}{24} = 127.9.....\); an integer greater than \(127.9\) is \(128\)
Therefore least integer greater than \(3070\) and divisible by \(24\) is \(24*128 = 3072\)
option A
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Re: If the least common multiple of m and n is 24, then what is [#permalink] New post 17 Jul 2018, 14:13
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Carcass wrote:
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



we are asked to find out the number divisible by 24 and the the number has to be larger than 3070.

Step 1 : divide 3070 by 24.

we have 127 and the remainder is 22.

So , if we deduct 22 from 3070 , the result will be evenly divisible by 24

The number after deduction : 3070 - 22 = 3048.

Step 2: add 24 to 3048.

So , 3048 +24 = 3072. surely , it is divisible by 24.

Thus the number larger than 3070 is 3072, which is divisible by 24.

Option A is the answer.

Hope it's clear.
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Re: If the least common multiple of m and n is 24, then what is [#permalink] New post 21 Sep 2019, 10:35
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If 24 is LCM of m and n then 24 is divisible by m and n.
Hence the answer should be divisible by 24 which means the answer should be divisible by 2,3 and 4.
Options A and C are divisible by 2,3 and 4. But since the question asks the first integer larger than 3070, Option A is the correct answer
Re: If the least common multiple of m and n is 24, then what is   [#permalink] 21 Sep 2019, 10:35
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