Question

what is the lcm and hcf of 20 and 36​

Answer 1

As per the data given in the question,

We have to determine the LCM and HCF of 20 and 36.

As we know that,

LCM means Lowest common multiple, LCM of two or more than two numbers are those numbers which is a lowest multiple of all the given number.

Or in simple words we can say that, LCM of two number is that lowest number which comes firstly in table of both numbers.

HCF means Highest Common factor.

HCF of two number is that greatest number which completely divides both the number.

So, we will use prime factorisation for finding LCM and HCF.

Prime factorisation of 20 and 36 will be,

$20 = 5\times 2 \times 2\\36 = 2\times3\times2\times3\\LCM = 5\times2\times2\times3\times3 \\LCM = 180\\HCF = 2\times2 \:(common\:number\:in\:factorisation\:of \:both\:digits)\\HCF = 4$

Hence, LCM of 20 and 36 will be 180 while HCF of 20 and 36 will be 4

Answer 2

Given: The numbers are$20 and 36$.

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

We are solving in the following way:

We have,

The numbers are$20 and 36$

The LCM of the above numbers will be:

Prime Factorization of $20$ is:

$2 \times2 \times5 => 22 \times 51$

Prime Factorization of $36$ is:

$2 \times2 \times 3 \times 3 => 22 \times 32$

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

$2, 2, 3, 3, 5$

Multiplying these factors together to find the LCM:

LCM = $2 \times 2 \times 3 \times 3 \times 5 = 180$

Therefore,

LCM$(20, 36) = 180$

The HCF of the above numbers will be:

The factors of $20$ are: $1, 2, 4, 5, 10, 20$

The factors of $36$ are: $1, 2, 3, 4, 6, 9, 12, 18, 36$

As we know that the greatest common divisor of two or more integers is the largest positive integer that divides each of the integers.

So, the greatest common factor is $4.$

Hence, the HCF and LCM of the above numbers will be $4$and$180$.