Question

the LCM and the HCF of the numbers 28 and 42 are in the ratio

Answer 1

LCM =84

HCF =14 ratio =84:14

Answer 2

Answer:

HCF(28 and 42)=14

LCM(28 and 42)=84

Ratio of HCF and LCM is 1:6

Step-by-step explanation:

Given : Numbers 28 and 42

To find : The HCF and LCM of 28 and 42 in ratio.

Solution : Using the fundamental theorem of arithmetic is represented as product of prime factors

First we find the prime factors of 28 and 42

$28= 2\times 2\times 7$

$42= 2 \times 3 \times 7$

HCF is the highest common factor of 28 and 42 is 2×7=14

HCF(28 and 42)=14

We know, Product of two numbers = HCF × LCM

Product of two numbers = $28\times42= 1176$

Product of two numbers = HCF × LCM

$1176=14\times LCM$

$LCM=\frac{1176}{14}$

$LCM=84$

LCM(28 and 42)=84

Therefore, Ratio of HCF and LCM is 14:84 or 1:6.