Least Common Multiple of 27 and 30

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 27 and 30 the smallest integer that is 270 that is divisible by both numbers.

Least Common Multiple (LCM) of 27 and 30 is 270.

LCM(27,30) = 270

LCM of 27 and 30

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

LCM of:
and

Least Common Multiple of 27 and 30

LCM of 27 and 30 is 270

Least common multiple can be found by multiplying the highest exponent prime factors of 27 and 30. First we will calculate the prime factors of 27 and 30.

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

Prime Factorization of 30


2 30
3 15
5 5
1

Prime factors of 30 are 2, 3,5. Prime factorization of 30 in exponential form is:

30 = 21×31×51

Now multiplying the highest exponent prime factors to calculate the LCM of 27 and 30.

LCM(27,30) = 21×33×51
LCM(27,30) = 270

Factors of 27

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

1, 3, 9, 27

Factors of 30

List of positive integer factors of 30 that divides 30 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30

Least Common Multiple of 27 and 30 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27 and 30, than apply into the LCM equation.

GCF(27,30) = 3
LCM(27,30) = ( 27 × 30) / 3
LCM(27,30) = 810 / 3
LCM(27,30) = 270

Properties of LCM 27 and 30

(i) The LCM of 30 and 27 is associative

LCM of 27 and 30 = LCM of 30 and 27

Related Least Common Multiples of 27

Related Least Common Multiples of 30

Frequently Asked Questions on LCM of 27 and 30

1. What is the LCM of 27 and 30?

Answer: LCM of 27 and 30 is 270.

2. 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.

3. What are the Factors of 30?

Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.

4. How to Find the LCM of 27 and 30?

Answer:

Least Common Multiple of 27 and 30 = 270

Step 1: Find the prime factorization of 27

27 = 3 x 3 x 3

Step 2: Find the prime factorization of 30

30 = 2 x 3 x 5

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 270 = 2 x 3 x 3 x 3 x 5

Step 4: Therefore, the least common multiple of 27 and 30 is 270.