Find the least number which when divided by 35, 56 and 91 leaves the same remainder

Least number which can be divided by 35, 56 and 91 is LCM of 35, 56 and 91.

Prime factorization of 35, 56 and 91 is:

35 = 5 × 7

$56=2^{3} \times 7$

91 = 7 × 13

LCM = product of greatest power of each prime factor involved in the numbers $=2^{3} \times 5 \times 7 \times 13=3640$

Least number which can be divided by 35, 56 and 91 is 3640.

Least number which when divided by 35, 56 and 91 leaves the same remainder 7 is 3640 + 7 = 3647.

Thus, the required number is 3647.