LCM of 36 and 42
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 36 and 42 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 36 and 42.
What is LCM of 36 and 42
Given Numbers are 36, 42
We can find the LCM of 36, 42 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 36 and 42
Multiples of 36 =36,72,108,144,180,216,252,288,324,360,396,432,468,504,540,576,612,
Multiples of 42 =42,84,126,168,210,252,294,336,378,420,462,504,546,588,630,672,714,
Now, get the least common multiple of 36, 42 which is 252
So, the LCM of 36, 42 is 252.
Least Common Multiple (LCM) of 36 and 42 with the help of Prime Factorisation
One method for determining the LCM of 36 and 42 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 36's prime factorization:
| 2 | 36 |
| 2 | 18 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 36 are 2,3.
36 = 22×32
And this is 42's prime factorization:
| 2 | 42 |
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 42 are 2, 3,7.
42 = 21×31×71
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: 2,3,7
.22×32×71 = 252
This shows that the LCM of 36 and 42 is 252.
How to Calculate the LCM of 36 and 42 Using Common Multiples
The first step in determining the Least Common Multiple of 36 and 42 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 36 and 42:
Lets look at the first ten multiples of these numbers, 36 and 42:
36,72,108,144,180,216,252,288,324,612 are the first ten multiples of 36.
42,84,126,168,210,252,294,336,378,714 are the first ten multiples of 42.
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 36 and 42, for example, are 432, 612, and 672. 252 is the least common multiple since it is the smallest.
36 and 42 have an LCM of 252.
Least Common Multiple of 36 and 42 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 36 and 42, than apply into the LCM equation.
GCF(36,42) = 6
LCM(36,42) = ( 36 × 42) / 6
LCM(36,42) = 1512 / 6
LCM(36,42) = 252
Related Least Common Multiples of 36
Related Least Common Multiples of 42
Frequently Asked Questions on LCM of 36 and 42
1. What is the LCM of 36 and 42?
The LCM of 36 and 42 is 252.
2. How to find the lowest common multiple of 36 and 42?
To find the lowest common multiple of 36 and 42, 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 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.
4. What are the Factors of 42?
Answer: Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. There are 8 integers that are factors of 42. The greatest factor of 42 is 42.
5. How to Find the LCM of 36 and 42?Answer:
Least Common Multiple of 36 and 42 = 252
Step 1: Find the prime factorization of 36
36 = 2 x 2 x 3 x 3
Step 2: Find the prime factorization of 42
42 = 2 x 3 x 7
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 36 and 42 is 252.