# What will be the Least number? If

The least number which when divided by 48, 64, 90, 120 will leave remainders 38, 54, 80, 110 respectively, is

- 2870
- 2860
- 2890
- 2880

**Answer:(3) 2890
Explanation:-
**The LCM of 48 , 64, 90 and 120

48 = 2 x 2 x 2 x 2 x 3

64 = 2 x 2 x 2 x 2 x 2 x 2

90 = 2 x 3 x 3 x 5

120 = 2 x 2 x 2 x 3 x 5

LCM = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5

The LCM of 48, 64, 90 and 120 is 2880

Remainder –

48 – 38 = 10, 64 – 54 = 10, 90 – 80 = 10, 120 – 110 = 10

Thus, the least number is 2880 + 10 = 2890

Hence, the number is 2890.