LCM of 15 and 21
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 15 and 21 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 105 as output. Here you can check the answer for Find the LCM of 15 and 21.
What is LCM of 15 and 21
Given Numbers are 15, 21
We can find the LCM of 15, 21 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 15 and 21
Multiples of 15 =15,30,45,60,75,90,105,120,135,150,165,180,195,210,225,240,255,
Multiples of 21 =21,42,63,84,105,126,147,168,189,210,231,252,273,294,315,336,357,
Now, get the least common multiple of 15, 21 which is 105
So, the LCM of 15, 21 is 105.
Least Common Multiple (LCM) of 15 and 21 with the help of Prime Factorisation
One method for determining the LCM of 15 and 21 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 15's prime factorization:
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 15 are 3,5.
15 = 31×51
And this is 21's prime factorization:
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 21 are 3,7.
21 = 31×71
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: 3,5,7
.31×51×71 = 105
This shows that the LCM of 15 and 21 is 105.
How to Calculate the LCM of 15 and 21 Using Common Multiples
The first step in determining the Least Common Multiple of 15 and 21 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 15 and 21:
Lets look at the first ten multiples of these numbers, 15 and 21:
15,30,45,60,75,90,105,120,135,255 are the first ten multiples of 15.
21,42,63,84,105,126,147,168,189,357 are the first ten multiples of 21.
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 15 and 21, for example, are 180, 255, and 336. 105 is the least common multiple since it is the smallest.
15 and 21 have an LCM of 105.
Least Common Multiple of 15 and 21 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15 and 21, than apply into the LCM equation.
GCF(15,21) = 3
LCM(15,21) = ( 15 × 21) / 3
LCM(15,21) = 315 / 3
LCM(15,21) = 105
Related Least Common Multiples of 15
Related Least Common Multiples of 21
Frequently Asked Questions on LCM of 15 and 21
1. What is the LCM of 15 and 21?
The LCM of 15 and 21 is 105.
2. How to find the lowest common multiple of 15 and 21?
To find the lowest common multiple of 15 and 21, we have to get the multip;es of both numbers and identify the least common multiple in them which is 105.
3. What are the Factors of 15?
Answer: Factors of 15 are 1, 3, 5, 15. There are 4 integers that are factors of 15. The greatest factor of 15 is 15.
4. What are the Factors of 21?
Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.
5. How to Find the LCM of 15 and 21?Answer:
Least Common Multiple of 15 and 21 = 105
Step 1: Find the prime factorization of 15
15 = 3 x 5
Step 2: Find the prime factorization of 21
21 = 3 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 105 = 3 x 5 x 7
Step 4: Therefore, the least common multiple of 15 and 21 is 105.