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.


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