Question

Find the LCM and HCF of the following pairs of integers and verify in each case that $LCM\times HCF=Productoftwonumbers$: $455and78$.

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 $455and78$.

Factorization of $455and78$:

Factorizing $455$we get $455=5\times 7\times 13$.

Factorizing $78$ we get $78=2\times 3\times 13$.

Finding LCM and HCF:

Here the HCF = $13$ and LCM = $5\times 13\times 7\times 2\times 3=2730$.

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

Here $LCM\times HCF=2730\times 13=35490$.

and Product of the given numbers = $455\times 78=35490$.

Hence, $LCM\times HCF=Productofthegivennumbers$.