How to Find the LCM of 972 and 978?

LCM of 972 and 978

Created By : Bhagya
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

It is easy to find the LCM of 972 and 978 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 158436 as output. Here you can check the answer for Find the LCM of 972 and 978.

What is LCM of 972 and 978

Given Numbers are 972, 978

We can find the LCM of 972, 978 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 972 and 978

Multiples of 972 =972,1944,2916,3888,4860,5832,6804,7776,8748,9720,10692,11664,12636,13608,14580,15552,16524,

Multiples of 978 =978,1956,2934,3912,4890,5868,6846,7824,8802,9780,10758,11736,12714,13692,14670,15648,16626,

Now, get the least common multiple of 972, 978 which is 158436

So, the LCM of 972, 978 is 158436.

Least Common Multiple (LCM) of 972 and 978 with the help of Prime Factorisation

One method for determining the LCM of 972 and 978 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:

Here is 972's prime factorization:

2	972
2	486
3	243
3	81
3	27
3	9
3	3
	1

Prime factors of 972 are 2,3.

972 = 2²×3⁵

And this is 978's prime factorization:

2	978
3	489
163	163
	1

Prime factors of 978 are 2, 3,163.

978 = 2¹×3¹×163¹

When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered: 2,3,163

2²×3⁵×163¹ = 158436

This shows that the LCM of 972 and 978 is 158436.

How to Calculate the LCM of 972 and 978 Using Common Multiples

The first step in determining the Least Common Multiple of 972 and 978 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 972 and 978:

Lets look at the first ten multiples of these numbers, 972 and 978:

972,1944,2916,3888,4860,5832,6804,7776,8748,16524 are the first ten multiples of 972.

978,1956,2934,3912,4890,5868,6846,7824,8802,16626 are the first ten multiples of 978.

You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 972 and 978, for example, are 11664, 16524, and 15648. 158436 is the least common multiple since it is the smallest.

972 and 978 have an LCM of 158436.

Least Common Multiple of 972 and 978 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 972 and 978, than apply into the LCM equation.

GCF(972,978) = 6
LCM(972,978) = ( 972 × 978) / 6
LCM(972,978) = 950616 / 6
LCM(972,978) = 158436

Related Least Common Multiples of 972

Related Least Common Multiples of 978

Frequently Asked Questions on LCM of 972 and 978

1. What is the LCM of 972 and 978?

The LCM of 972 and 978 is 158436.

2. How to find the lowest common multiple of 972 and 978?

To find the lowest common multiple of 972 and 978, we have to get the multip;es of both numbers and identify the least common multiple in them which is 158436.

3. What are the Factors of 972?

Answer: Factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972. There are 18 integers that are factors of 972. The greatest factor of 972 is 972.

4. What are the Factors of 978?

Answer: Factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978. There are 8 integers that are factors of 978. The greatest factor of 978 is 978.