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Question

Find the least number which when divided by 35,56 and 91 leaves the same remainder 7 in each case.

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Solution

The smallest number which when divided by 35,56 and 91= LCM of 35,56 and 91
35=5×7
56=2×2×2×7
91=7×13
LCM =7×5×2×2×2×13=3640
The smallest number that when divided by 35,56,91 leaves a remainder 7 in each case =3640+7=3647.

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