Question

Find the LCM and HCF of the following pairs of integers and verify in each case that $LCM\times HCF=Productoftwonumbers$:$408and170$.

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 data:

Given numbers are $408and170$.

Factorization of $408and170$:

Factorizing $408$ we get, $408=2\times 2\times 2\times 3\times 17$.

Factorizing $170$ we get, $170=2\times 5\times 17$.

Finding LCM and HCF:

Here the HCF = $2\times 17=34$.

LCM = $2\times 2\times 2\times 3\times 5\times 17$ = $2040$.

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

Here, $LCM\times HCF=34\times 2040=69360$.

and Product of the given numbers: $408\times 170=69360$.

Hence, $LCM\times HCF=Productofthegivennumbers$.