Question

Find a combination of positive integers a b c and d such that their sum is 1000, And their LCM is the least amongst LCMs of all such combinations.

Answer 1

Minimum LCM will be when all four are equal. a = b = c = d = 1000/4 = 250.

LCM(a, b, c, d) = 250.

Since all numbers are equal, the LCM is one of the numbers.

Suppose one number, say "a" is decreased by x then one of b, c or d has to increase at least by 1. Then LCM will be more than 250.

<br />For such questions involving multiple integers , try a combination when all numbers are equal.

<br />Then try other combinations. You will get some understanding.

Answer 2

Answer:

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