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.