Question

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

Answer 1

The required number $=LCM$of $(35,56,91)+7$

We have,

$35=5\times 7$

$56=2^3\times 7$

$91=13\times 7$

$LCM$of $(35,56,91)=5\times 8\times 13\times 7=3640$

The required number $=3640+7=3647$