Question

Find the least number which when divided
by 33. 44 and 55 leaves remainders 31,42
and 53. respectively​

Answer 1

Let us see the relation between the pairs of numbers if there is any:

36–25 = 11

48–37 = 11

64–53 = 11

The difference is 11, so there is a pattern

Next find the LCM of 36, 48 and 64

36 = 2x2x3x3

48 = 2x2x2x2x3

64= 2x2x2x2x2x2

So LCM = 2^6x3^2 = 576

The deduct 11 from 576 to get 565, which is the required number.

Check: 565/36= 15Q + 25R

565/48 = 11Q + 37R

565/64 = 8Q + 53R

Required Number is 565.