Find the least number which when divided by 35, 36 and 91 leaves the same remainder 7 in each case.

Find the LCM of the numbers (the least number which all the given numbers divides) -

Prime factorization of numbers -

35 = 5 × 7

36 = 2 × 2 × 3 × 3

91 = 7 × 13

LCM of given numbers = product of prime factors with highest powers = 2² × 3² × 5 × 7 × 13 = 3640.

∵ required remainder is 7.

We need to add 7 to the LCM of numbers.

∴ the least number that leaves remainder 7 will be 3640 + 7 = 3647.