A heap of pebbles when made up into group of 32, 40, 72, leaves the remainder 10, 18 and 50 respectively. Find least number of pebbles in the heaps.

A. 1440

B. 1420

C. 1418

D. 1422

Answer: Option C

Solution(By Examveda Team)

In this type of problem we find the difference of divisors and their remainders.
Here difference,
32 - 10 = 22
40 - 18 = 22
72 - 50 = 22
Here, in each case difference is same i.e. 22
Then required number of pebbles is given by
[(LCM of 32, 40, 72) -22]

32 = 2 × 2 × 2 × 2 × 2
40 = 2 × 2 × 2 × 5
72 = 2 × 2 × 2 × 3 × 3
Hence,
LCM = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 5 = 1440
Thus,
Required number of pebbles,
= 1440 - 22
= 1418