# Find out the smallest no. which on division by 24, 32 and 36 gives 19, 27 and 31 as remainder respectively.

(a) 283

(b) 273

(c) 281

(d) 285

**Answer: (a) 283 **

**Solution:**

The Factors of 24 = 2 x 2 x 2 x 3

The Factors of 32 = 2 x 2 x 2 x 2 x 2

The Factors of 36 = 2 x 2 x 3 x 3

Then, the LCM of 24, 32 and 36 = 2 x 2 x 2 x 2 x 2 x 3 x 3

= 288

The difference of 24 – 19 = 32 – 27 = 36 – 31 = 5

So, the smallest number = 288 – 5

= 283

Hence, the correct answer is option (a) 283.