Question

Find the HCF and LCM of 240, 500 and 120.
answer fast plz​

Answer 1

Given: The numbers are$240, 500, \ and\ 120.$

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

We are solving in the following way:

We have,

The numbers are$240, 500, \ and\ 120.$

a) The HCF of the above numbers will be:

The factors of $120$ are: $1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120$

The factors of $240$ are: $1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240$

The factors of $500$are: $1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500$

As we know that the greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

From the above concept, we can say that the greatest common factor is$20$.

b) The LCM of the above numbers will be:

First, we will list all prime factors for each number.

Prime Factorization of $120$is:

$2 \times 2 \times 2 \times 3 \times 5 => 2^3 \times 3^1 \times 5^1$

Prime Factorization of $240$is:

$2 \times 2 \times 2 \times 2 \times 3 \times 5 => 2^4 \times 3^1 \times 5^1$

Prime Factorization of $500$is:

$2 \times 2 \times 5 \times 5 \times 5 => 2^2 \times 5^3$

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:

$2, 2, 2, 2, 3, 5, 5, 5$

Multiplying these factors together to find the LCM.

LCM = $2 \times 2 \times 2 \times 2 \times 3 \times 5 \times 5 \times 5 = 6000$

Hence, we get,

a) HCF $=20$

b) LCM $=6000$