Question

5. Find HCF and LCM of following pairs of integers
by prime factorisation method and verify that LCM
x HCF = Product of the two numbers:
(iii) 77, 979.​

Answer 1

Answer:

Hence verified.

Step-by-step explanation:

Given numbers:

• 77 and 979

Finding the HCF using Prime factorisation method:

• 77 = 7 × 11
• 979 = 11 × 89

HCF of 77 and 979 = 11

Finding the LCM using Prime factorisation method:

• 77 = 7 × 11
• 979 = 11 × 89

LCM of 77 and 979 = 7× 11 × 89

LCM of 77 and 979 = 6853

Verification:

LCM x HCF = Product of two numbers

Finding the product of LCM and HCF:

• LCM × HCF = 6856 × 11
• LCM × HCF = 75383

Finding the product of two numbers:

• Product of two numbers = 77 × 979
• Product of two numbers = 75383

Here,

LCM x HCF = Product of two numbers

→ 75383 = 75383

Answer 2

Answer:

Given :-

• Two numbers are 77 and 979.

To Find :-

• What is the HCM and LCM of the following pairs of integers by prime factorisation method and verify that with LCM × HCF = Product of two numbers.

Solution :-

First, we have to find the HCF and LCM by prime factorisation,

➦ For HCF,

● 77 = 7 × 11

● 979 = 89 × 11

Hence, the common factors are,

➠ 11

➦ For LCM,

● 77 = 7 × 11

● 979 = 89 × 11

Hence, the common factors are,

⇒ 7 × 89 × 11

⇒ 623 × 11

➠ 6853

Now, we have to verify,

Given :

• HCF = 11
• LCM = 6853
• Product of two numbers = 77 , 979

As we know that,

✯LCM × HCF=Product of two number✯

According to the question by using the formula we get,

↦ 6853 × 11 = 77 × 979

➦ 75383 = 75383

Hence, Verified ✔