Students can practice TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.6 to get the best methods of solving problems.

## TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Exercise 3.6

Question 1.

Find the LCM and HCF of the following numbers.

(i) 15, 24

(ii) 8, 25

(iii) 12,48

check their relationship.

Answer:

(i) Factors of 15= 3 × 5

Factors of 24 = 3 × 2 × 2 × 2

LCM of 15 and 24 = 3 × 5 × 2 × 2 × 2= 120

HCF of 15 and 24 = 3

LCM × HCF = 120 × 3 = 360

Product of the two numbers = 15 × 24 = 360

∴ LCM × HCF = Product of the two numbers

(ii) Factors of 8 = 2 × 2 × 2

Factors of 25 = 5 × 5

LCM of 8 and 25 = 2 × 2 × 2 × 5 × 5 = 200

HCF of 8 and 25 = 1

∴ LCM × HCF = 200 × 1 = 200

Product of the two numbers = 8 × 25 = 200

∴ LCM × HCF = Product of the two numbers

(iii)

LCM of 12 and 48 = 2 × 2 × 3 × 2 × 2 = 48

HCF of 12 and 48 = 2 × 2 × 3 = 12

LCM × HCF = 12 × 48576

Product of the two numbers = 12 × 48 = 576

∴ LCM × HCF = Product of the two numbers

Question 2.

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

Answer:

Product of the two numbers = 7776

LCM of two numbers = 216

We know, LCM × HCF

= Product of the two numbers

∴216 × HCF = 7776

∴HCF = \(\frac{7776}{216}\) = 36

Question 3.

The product of two numbers is 3276.

If their HCF is 6, find their LCM.

Answer:

Product of the two numbers = 3276

HCF of the two numbers = 6

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

LCM × 6 = 3276

∴ LCM = \(\frac{3276}{6}\) = 3276

Question 4.

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

Answer:

The HCF of two numbers = 6

The LCM of two numbers = 36

One of the numbers = 12

Let the other number be x.

HCF × LCM = 6 × 36

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

∴ x = \(\frac{6 \times 36}{12}\) = 18

∴ The other number is 18.