LCM of 72 and 77
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 72 and 77 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 5544 as output. Here you can check the answer for Find the LCM of 72 and 77.
What is LCM of 72 and 77
Given Numbers are 72, 77
We can find the LCM of 72, 77 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 72 and 77
Multiples of 72 =72,144,216,288,360,432,504,576,648,720,792,864,936,1008,1080,1152,1224,
Multiples of 77 =77,154,231,308,385,462,539,616,693,770,847,924,1001,1078,1155,1232,1309,
Now, get the least common multiple of 72, 77 which is 5544
So, the LCM of 72, 77 is 5544.
Least Common Multiple (LCM) of 72 and 77 with the help of Prime Factorisation
One method for determining the LCM of 72 and 77 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 77's prime factorization:
| 7 | 77 |
| 11 | 11 |
| 1 |
Prime factors of 77 are 7,11.
77 = 71×111
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, 7,11
.23×32×71×111 = 5544
This shows that the LCM of 72 and 77 is 5544.
How to Calculate the LCM of 72 and 77 Using Common Multiples
The first step in determining the Least Common Multiple of 72 and 77 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 72 and 77:
Lets look at the first ten multiples of these numbers, 72 and 77:
72,144,216,288,360,432,504,576,648,1224 are the first ten multiples of 72.
77,154,231,308,385,462,539,616,693,1309 are the first ten multiples of 77.
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 77, for example, are 864, 1224, and 1232. 5544 is the least common multiple since it is the smallest.
72 and 77 have an LCM of 5544.
Least Common Multiple of 72 and 77 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 77, than apply into the LCM equation.
GCF(72,77) = 1
LCM(72,77) = ( 72 × 77) / 1
LCM(72,77) = 5544 / 1
LCM(72,77) = 5544
Related Least Common Multiples of 72
Related Least Common Multiples of 77
Frequently Asked Questions on LCM of 72 and 77
1. What is the LCM of 72 and 77?
The LCM of 72 and 77 is 5544.
2. How to find the lowest common multiple of 72 and 77?
To find the lowest common multiple of 72 and 77, we have to get the multip;es of both numbers and identify the least common multiple in them which is 5544.
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 77?
Answer: Factors of 77 are 1, 7, 11, 77. There are 4 integers that are factors of 77. The greatest factor of 77 is 77.
5. How to Find the LCM of 72 and 77?Answer:
Least Common Multiple of 72 and 77 = 5544
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 77
77 = 7 x 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 5544 = 2 x 2 x 2 x 3 x 3 x 7 x 11
Step 4: Therefore, the least common multiple of 72 and 77 is 5544.