# Find the Least Number

Find the least number which when divided by 12,18,36, and 45 leaves the remainder 8,14,32, and 41 respectively

- 178
- 186
- 176
- 180

**Answer: (3) 176**

**Explanation:-**

The LCM of 12, 18, 36 and 45

Factors of 12 = 2 x 2 x 3

Factors of 18 = 2 x 3 x 3

Factors of 36 = 2 x 2 x 3 x 3

Factors of 45 = 3 x 3 x 5

The LCM = 2 x 2 x 3 x 3 x 5 = 180

Remainder = 12 – 8 = 4, 18 – 14 = 4, 36 – 32 = 4 and 45 – 41 = 4

The number is 180 – 4 = 176

Hence, the answer is (3) 176