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Least Common Multiple of 21 and 27

Free LCM Calculator determines the least common multiple (LCM) between 21 and 27 the smallest integer that is 189 that is divisible by both numbers.

Least Common Multiple (LCM) of 21 and 27 is 189.

LCM(21,27) = 189

LCM of 21 and 27

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple (LCM) of 21 and 27 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 27. First we will calculate the prime factors of 21 and 27.

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 27


3 27
3 9
3 3
1

Prime factors of 27 are 3. Prime factorization of 27 in exponential form is:

27 = 33

Now multiplying the highest exponent prime factors to calculate the LCM of 21 and 27.

LCM(21,27) = 33×71
LCM(21,27) = 189

Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1, 3, 7, 21

Factors of 27

List of positive integer factors of 27 that divides 27 without a remainder.

1, 3, 9, 27

Least Common Multiple of 21 and 27 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 27, than apply into the LCM equation.

GCF(21,27) = 3
LCM(21,27) = ( 21 × 27) / 3
LCM(21,27) = 567 / 3
LCM(21,27) = 189

Properties of LCM 21 and 27

(i) The LCM of 27 and 21 is associative

LCM of 21 and 27 = LCM of 27 and 21

Frequently Asked Questions on LCM of 21 and 27

1. What is the LCM of 21 and 27?

Answer: LCM of 21 and 27 is 189.

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 27?

Answer: Factors of 27 are 1, 3, 9, 27. There are 4 integers that are factors of 27. The greatest factor of 27 is 27.

4. How to Find the LCM of 21 and 27?

Answer:

Least Common Multiple of 21 and 27 = 189

Step 1: Find the prime factorization of 21

21 = 3 x 7

Step 2: Find the prime factorization of 27

27 = 3 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 = 189 = 3 x 3 x 3 x 7

Step 4: Therefore, the least common multiple of 21 and 27 is 189.