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.