Question

Find the LCM and HCF of the following pairs of integers and verify in each case that $LCM\times HCF=Productsofthenumbers:510and92$.

Answer 1

Step 1: Finding the LCM and HCF:

Definition:

1. LCM means the smallest common multiple of two or more numbers.

2. HCF means the highest common factors of two or more numbers.

Given numbers are $510and92$.

Factorization of $510and92$:

Factorizing $510$we get $510=2\times 3\times 5\times 17$.

Factorizing $92$we get $92=2\times 2\times 23$.

Finding LCM and HCF:

Here, the HCF = $2$.

LCM = $2\times 2\times 3\times 5\times 17\times 23=23460$.

Step 2: Verifying $LCM\times HCF=Productoftwonumbers$:

Here, $LCM\times HCF=23460\times 2=46920$.

and product of the numbers = $510\times 92=46920$.

Hence, $LCM\times HCF=Productofthegivennumbers$.