Question

Find the least number which when divided by 12, 18, 24 and 30 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
1. 366
2. 634
3. 384
4. 364

Answer 1

Correct Answer - Option 4 : 364

Concept Used-

The least number which is divisible by several numbers is the LCM of such numbers.

Calculation-

The least number which is divisible by 12, 18, 24 and 30 = LCM of 12, 18, 24 and 30

⇒ 360

Now the least number which leaves remainder as 4 when divided by 12, 18, 24 and 30 = 360 + 4

⇒ 364

Now, 364 is divisible by 7.

∴ 364 is the required number.