1.

Prove the product of numebers = product of lcm and hcf for 35 and 80​

Answer»

Given:

To PROVE:

HCF × LCM = Product of 2 numbers

Solution:

By Prime Factorisation:

  • 35 = 5 × 7
  • 80 = 5 × 2 × 2 × 2 × 2 = 5 × 2⁴

In these 2 numbers, we observe that:

LCM = 5 × 7 × 2⁴ = 560

HCF = Common number in both given numbers = 5

Now, Let US verify their relation:

HCF × LCM = Product of 2 numbers

⇒ 5 × 560 = 35 × 80

⇒ 2800 = 2800

✬ HENCE PROVED ✬

KNOW MORE:

When numbers say, A and B are prime factorized,

  • HCF = A ∩ B
  • LCM = A ∪ B


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