Question

Find the least number which when divided by 16, 36, and 40 leaves 5 as the remainder in each case.

Answer 1

LCM of 16, 36, 40

1	16,  36,  40
2	8,  18,  20
2	4,    9,  10
2	2,    9,    5
2	1,    9,    5
3	1,    3,    5
3	1,    1,    5
5	1,    1,    1

LCM = 2⁵ × 3² × 5  = 16 × 9 × 5 = 720

⇒ LCM is 720

Now, Required Number = 720 + 5 = 725

∴ 725 is the least number which when divided by 16, 36, and 40 leaves 5 as the remainder in each case.