It is easy to find the LCM of 64 and 72 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 576 as output. Here you can check the answer for Find the LCM of 64 and 72.
Given Numbers are 64, 72
We can find the LCM of 64, 72 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 64 and 72
Multiples of 64 =64,128,192,256,320,384,448,512,576,640,704,768,832,896,960,1024,1088,
Multiples of 72 =72,144,216,288,360,432,504,576,648,720,792,864,936,1008,1080,1152,1224,
Now, get the least common multiple of 64, 72 which is 576
So, the LCM of 64, 72 is 576.
One method for determining the LCM of 64 and 72 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 64's prime factorization:2 | 64 |
2 | 32 |
2 | 16 |
2 | 8 |
2 | 4 |
2 | 2 |
1 |
Prime factors of 64 are 2.
64 = 26
And this 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
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
.26×32 = 576
This shows that the LCM of 64 and 72 is 576.
The first step in determining the Least Common Multiple of 64 and 72 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 64 and 72:
Lets look at the first ten multiples of these numbers, 64 and 72:
64,128,192,256,320,384,448,512,576,1088 are the first ten multiples of 64.
72,144,216,288,360,432,504,576,648,1224 are the first ten multiples of 72.
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 64 and 72, for example, are 768, 1088, and 1152. 576 is the least common multiple since it is the smallest.
64 and 72 have an LCM of 576.
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 64 and 72, than apply into the LCM equation.
GCF(64,72) = 8
LCM(64,72) = ( 64 × 72) / 8
LCM(64,72) = 4608 / 8
LCM(64,72) = 576
1. What is the LCM of 64 and 72?
The LCM of 64 and 72 is 576.
2. How to find the lowest common multiple of 64 and 72?
To find the lowest common multiple of 64 and 72, we have to get the multip;es of both numbers and identify the least common multiple in them which is 576.
3. What are the Factors of 64?
Answer: Factors of 64 are 1, 2, 4, 8, 16, 32, 64. There are 7 integers that are factors of 64. The greatest factor of 64 is 64.
4. 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.
5. How to Find the LCM of 64 and 72?Answer:
Least Common Multiple of 64 and 72 = 576
Step 1: Find the prime factorization of 64
64 = 2 x 2 x 2 x 2 x 2 x 2
Step 2: Find the prime factorization of 72
72 = 2 x 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 = 576 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3
Step 4: Therefore, the least common multiple of 64 and 72 is 576.