LCM of 72 and 76
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 72 and 76 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 1368 as output. Here you can check the answer for Find the LCM of 72 and 76.
What is LCM of 72 and 76
Given Numbers are 72, 76
We can find the LCM of 72, 76 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 72 and 76
Multiples of 72 =72,144,216,288,360,432,504,576,648,720,792,864,936,1008,1080,1152,1224,
Multiples of 76 =76,152,228,304,380,456,532,608,684,760,836,912,988,1064,1140,1216,1292,
Now, get the least common multiple of 72, 76 which is 1368
So, the LCM of 72, 76 is 1368.
Least Common Multiple (LCM) of 72 and 76 with the help of Prime Factorisation
One method for determining the LCM of 72 and 76 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 72's prime factorization:
| 2 | 72 |
| 2 | 36 |
| 2 | 18 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 72 are 2,3.
72 = 23×32
And this is 76's prime factorization:
| 2 | 76 |
| 2 | 38 |
| 19 | 19 |
| 1 |
Prime factors of 76 are 2,19.
76 = 22×191
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: 2,3,19
.23×32×191 = 1368
This shows that the LCM of 72 and 76 is 1368.
How to Calculate the LCM of 72 and 76 Using Common Multiples
The first step in determining the Least Common Multiple of 72 and 76 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 72 and 76:
Lets look at the first ten multiples of these numbers, 72 and 76:
72,144,216,288,360,432,504,576,648,1224 are the first ten multiples of 72.
76,152,228,304,380,456,532,608,684,1292 are the first ten multiples of 76.
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 72 and 76, for example, are 864, 1224, and 1216. 1368 is the least common multiple since it is the smallest.
72 and 76 have an LCM of 1368.
Least Common Multiple of 72 and 76 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72 and 76, than apply into the LCM equation.
GCF(72,76) = 4
LCM(72,76) = ( 72 × 76) / 4
LCM(72,76) = 5472 / 4
LCM(72,76) = 1368
Related Least Common Multiples of 72
Related Least Common Multiples of 76
Frequently Asked Questions on LCM of 72 and 76
1. What is the LCM of 72 and 76?
The LCM of 72 and 76 is 1368.
2. How to find the lowest common multiple of 72 and 76?
To find the lowest common multiple of 72 and 76, we have to get the multip;es of both numbers and identify the least common multiple in them which is 1368.
3. What are the Factors of 72?
Answer: Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. There are 12 integers that are factors of 72. The greatest factor of 72 is 72.
4. What are the Factors of 76?
Answer: Factors of 76 are 1, 2, 4, 19, 38, 76. There are 6 integers that are factors of 76. The greatest factor of 76 is 76.
5. How to Find the LCM of 72 and 76?Answer:
Least Common Multiple of 72 and 76 = 1368
Step 1: Find the prime factorization of 72
72 = 2 x 2 x 2 x 3 x 3
Step 2: Find the prime factorization of 76
76 = 2 x 2 x 19
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1368 = 2 x 2 x 2 x 3 x 3 x 19
Step 4: Therefore, the least common multiple of 72 and 76 is 1368.