LCM of 28 and 36
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 28 and 36 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 252 as output. Here you can check the answer for Find the LCM of 28 and 36.
What is LCM of 28 and 36
Given Numbers are 28, 36
We can find the LCM of 28, 36 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 28 and 36
Multiples of 28 =28,56,84,112,140,168,196,224,252,280,308,336,364,392,420,448,476,
Multiples of 36 =36,72,108,144,180,216,252,288,324,360,396,432,468,504,540,576,612,
Now, get the least common multiple of 28, 36 which is 252
So, the LCM of 28, 36 is 252.
Least Common Multiple (LCM) of 28 and 36 with the help of Prime Factorisation
One method for determining the LCM of 28 and 36 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 28's prime factorization:
| 2 | 28 |
| 2 | 14 |
| 7 | 7 |
| 1 |
Prime factors of 28 are 2,7.
28 = 22×71
And this is 36's prime factorization:
| 2 | 36 |
| 2 | 18 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 36 are 2,3.
36 = 22×32
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: 2,7,3
.22×32×71 = 252
This shows that the LCM of 28 and 36 is 252.
How to Calculate the LCM of 28 and 36 Using Common Multiples
The first step in determining the Least Common Multiple of 28 and 36 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 28 and 36:
Lets look at the first ten multiples of these numbers, 28 and 36:
28,56,84,112,140,168,196,224,252,476 are the first ten multiples of 28.
36,72,108,144,180,216,252,288,324,612 are the first ten multiples of 36.
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 28 and 36, for example, are 336, 476, and 576. 252 is the least common multiple since it is the smallest.
28 and 36 have an LCM of 252.
Least Common Multiple of 28 and 36 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 28 and 36, than apply into the LCM equation.
GCF(28,36) = 4
LCM(28,36) = ( 28 × 36) / 4
LCM(28,36) = 1008 / 4
LCM(28,36) = 252
Related Least Common Multiples of 28
Related Least Common Multiples of 36
Frequently Asked Questions on LCM of 28 and 36
1. What is the LCM of 28 and 36?
The LCM of 28 and 36 is 252.
2. How to find the lowest common multiple of 28 and 36?
To find the lowest common multiple of 28 and 36, we have to get the multip;es of both numbers and identify the least common multiple in them which is 252.
3. What are the Factors of 28?
Answer: Factors of 28 are 1, 2, 4, 7, 14, 28. There are 6 integers that are factors of 28. The greatest factor of 28 is 28.
4. What are the Factors of 36?
Answer: Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. There are 9 integers that are factors of 36. The greatest factor of 36 is 36.
5. How to Find the LCM of 28 and 36?Answer:
Least Common Multiple of 28 and 36 = 252
Step 1: Find the prime factorization of 28
28 = 2 x 2 x 7
Step 2: Find the prime factorization of 36
36 = 2 x 2 x 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 252 = 2 x 2 x 3 x 3 x 7
Step 4: Therefore, the least common multiple of 28 and 36 is 252.