LCM of 72 and 78
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 72 and 78 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 936 as output. Here you can check the answer for Find the LCM of 72 and 78.
What is LCM of 72 and 78
Given Numbers are 72, 78
We can find the LCM of 72, 78 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 72 and 78
Multiples of 72 =72,144,216,288,360,432,504,576,648,720,792,864,936,1008,1080,1152,1224,
Multiples of 78 =78,156,234,312,390,468,546,624,702,780,858,936,1014,1092,1170,1248,1326,
Now, get the least common multiple of 72, 78 which is 936
So, the LCM of 72, 78 is 936.
Least Common Multiple (LCM) of 72 and 78 with the help of Prime Factorisation
One method for determining the LCM of 72 and 78 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 78's prime factorization:
| 2 | 78 |
| 3 | 39 |
| 13 | 13 |
| 1 |
Prime factors of 78 are 2, 3,13.
78 = 21×31×131
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: 2,3,13
.23×32×131 = 936
This shows that the LCM of 72 and 78 is 936.
How to Calculate the LCM of 72 and 78 Using Common Multiples
The first step in determining the Least Common Multiple of 72 and 78 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 72 and 78:
Lets look at the first ten multiples of these numbers, 72 and 78:
72,144,216,288,360,432,504,576,648,1224 are the first ten multiples of 72.
78,156,234,312,390,468,546,624,702,1326 are the first ten multiples of 78.
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 78, for example, are 864, 1224, and 1248. 936 is the least common multiple since it is the smallest.
72 and 78 have an LCM of 936.
Least Common Multiple of 72 and 78 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 78, than apply into the LCM equation.
GCF(72,78) = 6
LCM(72,78) = ( 72 × 78) / 6
LCM(72,78) = 5616 / 6
LCM(72,78) = 936
Related Least Common Multiples of 72
Related Least Common Multiples of 78
Frequently Asked Questions on LCM of 72 and 78
1. What is the LCM of 72 and 78?
The LCM of 72 and 78 is 936.
2. How to find the lowest common multiple of 72 and 78?
To find the lowest common multiple of 72 and 78, we have to get the multip;es of both numbers and identify the least common multiple in them which is 936.
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 78?
Answer: Factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78. There are 8 integers that are factors of 78. The greatest factor of 78 is 78.
5. How to Find the LCM of 72 and 78?Answer:
Least Common Multiple of 72 and 78 = 936
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 78
78 = 2 x 3 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 936 = 2 x 2 x 2 x 3 x 3 x 13
Step 4: Therefore, the least common multiple of 72 and 78 is 936.