Question

Find the LCM and HCF of two integers 1015, 1165 ​

Answer 1

Step-by-step explanation:

lcm of 1015 and 1165 is 236495

and HCF is 5

Answer 2

Given: The two integers are$1015\ and\ 1165$.

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

We are solving in the following way:

We have,

The two integers are$1015\ and\ 1165$.

a) The LCM of the above integers will be:

Prime Factorization of  $1015$is:

$5 \times 7 \times 29 => 5^1 \times7^1 \times 29^1$

Prime Factorization of $1165$ is:

$5 \times 233 => 5^1 \times 233^1$

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:

$5, 7, 29, 233$

Multiplying these factors together to find the LCM:

LCM: $5 \times 7 \times 29 \times 233 = 236495$

In exponential form:

LCM $=5^1 \times 7^1 \times 29^1 \times 233^1 = 236495$

LCM = $236495$

Hence, the LCM of the above numbers is$236495$.

b) The HCF of $1015\ and\ 1165$ will be:

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.

The factors of $1015$ are: $1, 5, 7, 29, 35, 145, 203, 1015$

The factors of $1165$ are: $1, 5, 233, 1165$

Then the greatest common factor is $5$.

Hence, the LCM of the above numbers is$236495$.

And the HCF of the above numbers is$5$.