Extra Questions For Class 10 Maths Chapter 1 | Q6

This CBSE class 10 Maths Extra Practice Question is from the chapter Real Numbers. This question is about computing HCF and LCM of numbers using the prime factorisation method.

Question 6 : Find LCM and HCF of the following:
(i) 2⁵ × 5⁴ × 7² × 13⁶ and 2³ × 5⁶ × 7 × 17³
(ii) a⁵ × b² × c² × d⁵ and a⁷ × b³ × e × f³ where a, b, c, d, e and f are prime .

Video Solution

Explanatory Answer

How to compute HCF by Prime Factorisation Method?

HCF of two numbers is the product of LOWEST power of COMMON primes found in the numbers.

How to find LCM by Prime Factorisation Method?

LCM of two numbers is the product of HIGHEST power of ALL primes found in the numbers.

(i)LCM and HCF of 2⁵ × 5⁴ × 7² × 13⁶ and 2³ × 5⁶ × 7 × 17³

Notice that the two numbers are already prime factorized. That makes life really easy.
Let us compute HCF first.
The common primes in the two numbers are 2, 5, and 7.
The lowest power of 2, 5, and 7 are respectively 2³, 5⁴, and 7¹
∴ HCF of 2⁵ × 5⁴ × 7² × 13⁶ and 2³ × 5⁶ × 7 × 17³ is 2³ × 5⁴ × 7

Let us compute LCM next.
The primes found in the two numbers are 2, 5, 7, 13, and 17.
The highest power of 2, 5, 7, 13, and 17 are 2⁵, 5⁶, 7², 13⁶, and 17³ respectively.
∴ LCM of 2⁵ × 5⁴ × 7² × 13⁶ and 2³ × 5⁶ × 7 × 17³ is 2⁵ × 5⁶ × 7² × 13⁶ × 17³

(ii) Find the LCM and HCF of a⁵ × b² × c² × d⁵ and a⁷ × b³ × e × f³

Given: a, b, c, d, e, and f are prime numbers.
Let us compute HCF first.
The common primes in the two numbers are a and b.
The lowest power of a and b in the two numbers are a⁵ and b² respectively.
∴ HCF of a⁵ × b² × c² × d⁵ and a⁷ × b³ × e × f³ is a⁵ × b²

Let us compute LCM next.
The primes found in the two numbers are a, b, c, d, e, and f.
The highest power of a, b, c, d, e, and f are a⁷, b³, c², d⁵, e¹, and f³ respectively.
∴ LCM of a⁵ × b² × c² × d⁵ and a⁷ × b³ × e × f³ is a⁷ × b³ × c² × d⁵ × e × f³