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.