Question

For any 2 natural numbers, their LCM is always divisible by their HCF. State whether true or false.

• A. True
• B. False

Answer 1

The correct option is A

True

LCM is the lowest common multiple of the two numbers and HCF is the highest common factor.

Since HCF is a factor to both the numbers, then it will also be a factor to all of their multiples.

For eg- 14, 6

14= 2 x 7

6= 2 x 3

HCF of 14 and 6 will be 2.

This means that 2 is a factor of 14 and 6.

LCM of 14 and 6= 2 x 7 x 3= 42

42= 2 x 3 x 7

We can clearly see that 2 is also a factor of 42 (which is a multiple of 14 and 6)