LCM of 60 and 67
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 60 and 67 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 4020 as output. Here you can check the answer for Find the LCM of 60 and 67.
What is LCM of 60 and 67
Given Numbers are 60, 67
We can find the LCM of 60, 67 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 60 and 67
Multiples of 60 =60,120,180,240,300,360,420,480,540,600,660,720,780,840,900,960,1020,
Multiples of 67 =67,134,201,268,335,402,469,536,603,670,737,804,871,938,1005,1072,1139,
Now, get the least common multiple of 60, 67 which is 4020
So, the LCM of 60, 67 is 4020.
Least Common Multiple (LCM) of 60 and 67 with the help of Prime Factorisation
One method for determining the LCM of 60 and 67 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 60's prime factorization:
| 2 | 60 |
| 2 | 30 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 60 are 2, 3,5.
60 = 22×31×51
And this is 67's prime factorization:
| 67 | 67 |
| 1 |
Prime factors of 67 are 67.
67 = 671
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, 3,5,67
.22×31×51×671 = 4020
This shows that the LCM of 60 and 67 is 4020.
How to Calculate the LCM of 60 and 67 Using Common Multiples
The first step in determining the Least Common Multiple of 60 and 67 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 60 and 67:
Lets look at the first ten multiples of these numbers, 60 and 67:
60,120,180,240,300,360,420,480,540,1020 are the first ten multiples of 60.
67,134,201,268,335,402,469,536,603,1139 are the first ten multiples of 67.
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 60 and 67, for example, are 720, 1020, and 1072. 4020 is the least common multiple since it is the smallest.
60 and 67 have an LCM of 4020.
Least Common Multiple of 60 and 67 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 60 and 67, than apply into the LCM equation.
GCF(60,67) = 1
LCM(60,67) = ( 60 × 67) / 1
LCM(60,67) = 4020 / 1
LCM(60,67) = 4020
Related Least Common Multiples of 60
Related Least Common Multiples of 67
Frequently Asked Questions on LCM of 60 and 67
1. What is the LCM of 60 and 67?
The LCM of 60 and 67 is 4020.
2. How to find the lowest common multiple of 60 and 67?
To find the lowest common multiple of 60 and 67, we have to get the multip;es of both numbers and identify the least common multiple in them which is 4020.
3. What are the Factors of 60?
Answer: Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. There are 12 integers that are factors of 60. The greatest factor of 60 is 60.
4. What are the Factors of 67?
Answer: Factors of 67 are 1, 67. There are 2 integers that are factors of 67. The greatest factor of 67 is 67.
5. How to Find the LCM of 60 and 67?Answer:
Least Common Multiple of 60 and 67 = 4020
Step 1: Find the prime factorization of 60
60 = 2 x 2 x 3 x 5
Step 2: Find the prime factorization of 67
67 = 67
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4020 = 2 x 2 x 3 x 5 x 67
Step 4: Therefore, the least common multiple of 60 and 67 is 4020.