Question

find the HCF of 312 and 27 using Euclid's division algorithm find LCM and verify that LCM multiplied by HCF is equal to the product of two no

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Concept Introduction: LCM and HCF are basic concepts of Mathematics.

Given:

We have been Given:

$312 \\ 27$

To Find:

We have to Find: Prove that, Product of the two numbers is equal to the product of the LCM and HCF of the numbers.

Solution:

According to the problem, HCF of the numbers are,

$312 = 27 \times 11 + 15 \\ 27 = 15 \times 1 + 12 \\ 15 = 12 \times 1 + 3 \\ 12 = 3 \times 4 + 0$

therefore the HCF is

$3$

LCM of the numbers is

$2808$

therefore solving LHS first, product of the numbers is

$312 \times 27 = 8424$

solving RHS, product of the LCM and HCF of the numbers is

$2808 \times 3 = 8424$

hence LHS is equal to RHS, HENCE PROVED.

Final Answer: Product of the two numbers is equal to the product of the LCM and HCF of the numbers, Hence Proved.

#SPJ2