What is the least number which when divided by 16 36 and 40 leaves 5 as remainder in each case?

On subtracting 5 from each number:16 − 5 = 1136 − 5 = 3140 − 5 = 35The required number will be the least common multiple of 11, 31 and 35.L.C.M. of 11, 31 and 35 = 11×31×35                                       = 11935This is because they do not have any factor in common.

So, 11935 is the required number.

Find the least number which when divided by 16, 36, and 40 leaves 5 as the remainder in each case.

On subtracting 5 from each number:16 − 5 = 1136 − 5 = 3140 − 5 = 35The required number will be the least common multiple of 11, 31, and 35.L.C.M. of 11, 31 and 35 = 11×31×35= 11935This is because they do not have any factor in common.

So, 11935 is the required number.

Concept: Lowest Common Multiple

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