Question

HCF and LCM of 70,86,120,135
.​

Answer 1

Given: The numbers are$70,86,120,135$.

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

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.

We are solving in the following way:

We have,

The numbers are$70,86,120,135$.

a) The HCF of the above numbers will be:

First, we will find factors of the given numbers:

The factors of $70$ are: $1, 2, 5, 7, 10, 14, 35, 70$

The factors of $86$ are: $1, 2, 43, 86$

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

The factors of $135$ are: $1, 3, 5, 9, 15, 27, 45, 135$

From the above, we can see that $1$is the largest positive integer that divides each of the given numbers.

Then the greatest common factor(HCF) is$1$.

b) The LCM of the above numbers will be:

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

Prime Factorization of $70$is:

$2 \times 5 \times 7 => 2^1 \times 5^1 \times 7^1$

Prime Factorization of $86$is:

$2 \times 43 => 2^1 \times43^1$

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 $135$is:

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

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

$2, 2, 2, 3, 3, 3, 5, 7, 43$

Multiply these factors together to find the LCM.

$LCM = 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 5 \times 7 \times 43 = 325080$

Hence, we get$HCF=1\ and\ LCM=325080$