Question

find the smallest number which when divided by 1088, 640 and 100 leaves 3 as reminder in each case in

Answer 1

Given:

find the smallest number which when divided by 1088, 640 and 100 leaves 3 as a reminder in each case.

To find:

The required number

Solution:

Prime factors of 1088:

1088 = 2x2x2x2x2x2x17 = 2⁶ x 17

Prime factors of 640:

640 = 2x2x2x2x2x2x2x5 = 2⁷ x 5

Prime factors of 100:

100 = 2x2x5x5 = 2² x 5²

LCM = 2⁷ x 5² x 17 = 128 x 25 x 17 = 54400

54400 + 3 = 54403

Hence, the required answer is 54403