Exercise 3.6

1. Find the LCM and HCF of the following numbers?

(i) 15, 24 (ii) 8, 25 (iii) 12, 48

Check their relationship.

(i) Factors of 15 = ×

Factors of 24 = × × ×

LCM of 15 and 24 = × × × × =

HCF of 15 and 24 =

LCM × HCF = × =

Therefore, LCM × HCF = of the two numbers

(ii) Factors of 8 = × ×

Factors of 25 = ×

LCM of 8 and 25 = × × × × =

HCF of 8 and 25 =

LCM × HCF = × =

Product of the two numbers = × =

Therefore, LCM × HCF = of the two numbers

(iii) Factors of 12 = × ×

Factors of 48 = × × × ×

LCM of 12 and 48 = × × × × =

HCF of 12 and 48 = × × =

LCM × HCF = × =

Therefore, LCM × HCF = of the two numbers.

2. If the LCM of two numbers is 216 and their product is 7776, what will be its HCF?

Product of the two numbers =

LCM of two numbers =

We know, LCM × HCF

= Product of the two numbers

= × HCF =

HCF = 7776216 =

3. The product of two numbers is 3276. If their HCF is 6, find their LCM?

Product of the two numbers =

HCF of the two numbers =

We know, LCM × HCF = Product of the two numbers

LCM × =

Therefore, LCM = 32766 =

4. The HCF of two numbers is 6 and their LCM is 36. If one of the numbers is 12, find the other?

The HCF of two numbers =

The LCM of two numbers =

One of the numbers =

Let the other number be x.

HCF × LCM = ×

Product of the two numbers = 12 × x

We know, LCM × HCF = Product of the two numbers

6×36=12×x

(i.e.) 12×x=6×36

Therefore, x=6×36÷12 =

Therefore, the other number is .