Find the least possible number which when divided by 36, 49, 54 or 70 leaves remainders of 19, 32, 37 and 53, respectively.

Correct option is C

Given:

Required number leaves remainders:

36 → 19

49 → 32

54 → 37

70 → 53

Formula Used:

Let required number = LCM(36, 49, 54, 70) + respective difference

All remainders = Divisor − Remainder = Constant difference

Solution:

Each remainder is 17 less than the divisor:

36 - 19 = 17

49 - 32 = 17

54 - 37 = 17

70 - 53 = 17

So, the number - 17 is divisible by all:

Prime factorizations:

36 = $$2^2 \times 3^2$$​​

49 = $$7^2$$​​

54 = $$2 \times 3^3$$​​

70 = $$2 \times 5 \times 7$$​​

LCM = $$2^2 \times 3^3 \times 5 \times 7^2 = 4 \times 27 \times 5 \times 49 = 26460$$​​

Required number = 26460 - 17 = 26443