Question

What is the smallest number that, when divided by 35,56 and 91 leaves remainders of 7
in each case?
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Answer 1

Find the LCM of 35, 56 and 91. For that find the factors of

35 = 5x7

56 = 2x2x2x7

91 = 7x13

So the LCM = 2x2x2x7x5x13 = 3640.

The number you want is 3640+7 = 3647.

Check: 3647/35 = 104 + 7 as remainder.

3647/56 = 65 + 7 as remainder.

3647/91= 40 + 7 as remainder.

The answer is 3647.