Least Common Multiple of 21 and 28
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 21 and 28 the smallest integer that is 84 that is divisible by both numbers.
Least Common Multiple (LCM) of 21 and 28 is 84.
LCM(21,28) = 84
LCM of 21 and 28
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 21 and 28 by Prime method
- Least Common Multiple of 21 and 28 with GCF Formula
LCM of 21 and 28 is 84
Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 28. First we will calculate the prime factors of 21 and 28.
Prime Factorization of 21
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 21 are 3,7. Prime factorization of 21 in exponential form is:
21 = 31×71
Prime Factorization of 28
| 2 | 28 |
| 2 | 14 |
| 7 | 7 |
| 1 |
Prime factors of 28 are 2,7. Prime factorization of 28 in exponential form is:
28 = 22×71
Now multiplying the highest exponent prime factors to calculate the LCM of 21 and 28.
LCM(21,28) = 22×31×71
LCM(21,28) = 84
Factors of 21
List of positive integer factors of 21 that divides 21 without a remainder.
1, 3, 7, 21
Factors of 28
List of positive integer factors of 28 that divides 28 without a remainder.
1, 2, 4, 7, 14, 28
Least Common Multiple of 21 and 28 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21 and 28, than apply into the LCM equation.
GCF(21,28) = 7
LCM(21,28) = ( 21 × 28) / 7
LCM(21,28) = 588 / 7
LCM(21,28) = 84
Properties of LCM 21 and 28
(i) The LCM of 28 and 21 is associative
LCM of 21 and 28 = LCM of 28 and 21
Related Least Common Multiples of 21
Related Least Common Multiples of 28
Frequently Asked Questions on LCM of 21 and 28
1. What is the LCM of 21 and 28?
Answer: LCM of 21 and 28 is 84.
2. 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.
3. What are the Factors of 28?
Answer: Factors of 28 are 1, 2, 4, 7, 14, 28. There are 6 integers that are factors of 28. The greatest factor of 28 is 28.
4. How to Find the LCM of 21 and 28?
Answer:
Least Common Multiple of 21 and 28 = 84
Step 1: Find the prime factorization of 21
21 = 3 x 7
Step 2: Find the prime factorization of 28
28 = 2 x 2 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 = 84 = 2 x 2 x 3 x 7
Step 4: Therefore, the least common multiple of 21 and 28 is 84.
