Question

Find the HCF and L.CM. of the following numbers: (b) 496 and 1116​

Answer 1

Answer:

lcm= 4,464 hcf=124

Step-by-step explanation:

Answer 2

Given: The numbers are $496$and$1116$.

We have to find the HCF and LCM of the given numbers.

We are solving in the following way:

We have,

The numbers are $496$and$1116$

The HCF of the above numbers will be:

The factors of $496$ are: $1, 2, 4, 8, 16, 31, 62, 124, 248, 496$

The factors of $1116$ are: $1, 2, 3, 4, 6, 9, 12, 18, 31, 36, 62, 93, 124, 186, 279, 372, 558, 1116$

Then the greatest common factor is$124$.

The LCM of the above numbers will be:

Prime Factorization of $496$is:

$2 \times 2 \times 2 \times 2 \times 31 => 2^{4} \times 31^{1}$

Prime Factorization of $1116$is:

$2 \times 2 \times3 \times 3 \times 31 => 2^{2} \times 3^{2} \times 31^{1}$

For each prime factor, we will find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is:

$2, 2, 2, 2, 3, 3, 31$

Multiplying these factors together to find the LCM.

LCM = $2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 31 = 4464$

Hence, HCF of $496$and$1116$ is$124$ and LCM of $496$and$1116$ is$4464$.