Question

The least number which is exactly divisible by 4, 5, 8, 10 and 12 is:
1. 120
2. 150
3. 180
4. 240

Answer 1

Correct Answer - Option 1 : 120

Given:

Numbers 4, 5, 8, 10, 12

Concept Used:

Least Number divisible by a set of Number = Least common multiple (LCM) of that set of numbers

Calculation:

4 = 2²

5 = 5¹

8 = 2³

10 = 2¹ × 5¹

12 = 2² × 3¹

Least Common Multiple (LCM) of 4, 5, 8, 10, 12 = 2³ × 3¹ × 5¹ 

⇒ 8 × 3 × 5 = 120

∴ 120 is the least number which is exactly divisible by 4, 5, 8, 10, 12.

Least common multiple: The least common multiple of numbers is the smallest non-zero common numbers which are the multiple of all the numbers.