Question

3. The LCM of two numbers 42 and 77 is 462. What is their HCF?
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Answer 1

Answer:

HCF of 42 and 77 is 7.

Step-by-step explanation:

The explanation is in the attachment.

Answer 2

The HCF of the two numbers = 7

Given :

The LCM of two numbers 42 and 77 is 462

To find :

The HCF of two numbers

Concept :

HCF :

For the given two or more numbers HCF is the greatest number that divides each of the numbers

LCM :

For the given two or more numbers LCM is the least number which is exactly divisible by each of the given numbers

Relation between HCF and LCM :

HCF × LCM = Product of the numbers

Solution :

Step 1 of 2 :

Write down LCM

Here it is given that LCM of two numbers 42 and 77 is 462.

Step 2 of 2 :

Find the HCF

We know that

HCF × LCM = Product of the numbers

$\displaystyle \sf{ \implies HCF \times 462 = 42 \times 77}$

$\displaystyle \sf{ \implies HCF = \frac{42 \times 77}{462} }$

$\displaystyle \sf{ \implies HCF = \frac{42 }{6} }$

$\displaystyle \sf{ \implies HCF = 7 }$

Hence HCF of the two numbers = 7

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