Question

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

Answer 1

The smallest number which when divided by 35, 56 and 91 = $LCM(35,56,91)$

$35=5\times 7$

$56=2^3\times 7$

$91=7\times 13$

$LCM=2^3\times 5\times 7\times 13=3640$

$\text{The smallest number that when divided by 35, 56, 91 leaves a remainder 7 in each case = 3640 + 7 = 3647.}$