LCM of 16 and 21
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 16 and 21 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 336 as output. Here you can check the answer for Find the LCM of 16 and 21.
What is LCM of 16 and 21
Given Numbers are 16, 21
We can find the LCM of 16, 21 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 16 and 21
Multiples of 16 =16,32,48,64,80,96,112,128,144,160,176,192,208,224,240,256,272,
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 16, 21 which is 336
So, the LCM of 16, 21 is 336.
Least Common Multiple (LCM) of 16 and 21 with the help of Prime Factorisation
One method for determining the LCM of 16 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 16's prime factorization:
| 2 | 16 |
| 2 | 8 |
| 2 | 4 |
| 2 | 2 |
| 1 |
Prime factors of 16 are 2.
16 = 24
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:2, 3,7
.24×31×71 = 336
This shows that the LCM of 16 and 21 is 336.
How to Calculate the LCM of 16 and 21 Using Common Multiples
The first step in determining the Least Common Multiple of 16 and 21 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 16 and 21:
Lets look at the first ten multiples of these numbers, 16 and 21:
16,32,48,64,80,96,112,128,144,272 are the first ten multiples of 16.
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 16 and 21, for example, are 192, 272, and 336. 336 is the least common multiple since it is the smallest.
16 and 21 have an LCM of 336.
Least Common Multiple of 16 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 16 and 21, than apply into the LCM equation.
GCF(16,21) = 1
LCM(16,21) = ( 16 × 21) / 1
LCM(16,21) = 336 / 1
LCM(16,21) = 336
Related Least Common Multiples of 16
Related Least Common Multiples of 21
Frequently Asked Questions on LCM of 16 and 21
1. What is the LCM of 16 and 21?
The LCM of 16 and 21 is 336.
2. How to find the lowest common multiple of 16 and 21?
To find the lowest common multiple of 16 and 21, we have to get the multip;es of both numbers and identify the least common multiple in them which is 336.
3. What are the Factors of 16?
Answer: Factors of 16 are 1, 2, 4, 8, 16. There are 5 integers that are factors of 16. The greatest factor of 16 is 16.
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 16 and 21?Answer:
Least Common Multiple of 16 and 21 = 336
Step 1: Find the prime factorization of 16
16 = 2 x 2 x 2 x 2
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 = 336 = 2 x 2 x 2 x 2 x 3 x 7
Step 4: Therefore, the least common multiple of 16 and 21 is 336.