# Find the least number which when divided by 35,45 and 55 leaves the reminder 18,28 and 38

Find the least number which when divided by 35,45 and 55 leaves the reminder 18,28 and 38 respectively

(a) 2981

(b) 2670

(c) 3120

(d) 3448

**Answer: (d) 3448 **

**Explanation:-**

The factors of 35 = 5 x 7

The factors of 45 = 3 x 3 x 5

The factors of 55 = 5 x 11

Then, the L. C. M. of 35, 45 and 55 = 3 x 3 x 5 x 7 x 11

= 3465

The difference between divisor and remainder = 35 – 18 = 17, 45 – 28 = 17 & 55 – 38 = 17.

Then, required number = 3465 – 17

= 3448

Hence, the correct answer is option (d) 3448.