Question

Q4. Find the HCF and LCM of 30, 60 and 75 by Prime factorisation method-
(Ans HCF= 15, LCM= 300)​

Answer 1

Answer:

1. HCF of 30, 60 and 75 is 15.
2. LCM of 30, 60 and 75 is 300.

Step-by-step explanation:

To Find:

• The HCF and LCM of 30, 60 and 75 by prime factorisation method.

We know that:

1. HCF = Highest Common Factor
2. LCM = Lowest Common Multiple

Finding the HCF and LCM:

By prime factorisation.

• Factors of 30 = 2 × 3 × 5
• Factors of 60 = 2² × 3 × 5
• Factors of 75 = 3 × 5²

Here,

• Highest Common Factor = 3 × 5 = 15
• Lowest Common Multiple = 2² × 3 × 5² = 300

Hence,

1. HCF of 30, 60 and 75 is 15.
2. LCM of 30, 60 and 75 is 300.

Answer 2

Given :-

Numbers are 30,60 and 75

Solution :-

Factorization of 30 = 2 × 3 × 5

Factorization of 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5

Factorization of 75 = 3 × 5 × 5 = 3 × 5²

So,

LCM = 2² × 3 × 5² = 300

HCF = 3 × 5 = 15