Least Common Multiple of 27 and 10

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 10 the smallest integer that is 270 that is divisible by both numbers.

Least Common Multiple (LCM) of 27 and 10 is 270.

LCM(27,10) = 270

LCM of 27 and 10

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

LCM of:
and

Least Common Multiple of 27 and 10

LCM of 27 and 10 is 270

Least common multiple can be found by multiplying the highest exponent prime factors of 27 and 10. First we will calculate the prime factors of 27 and 10.

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 10


2 10
5 5
1

Prime factors of 10 are 2,5. Prime factorization of 10 in exponential form is:

10 = 21×51

Now multiplying the highest exponent prime factors to calculate the LCM of 27 and 10.

LCM(27,10) = 21×33×51
LCM(27,10) = 270

Factors of 27

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

1, 3, 9, 27

Factors of 10

List of positive integer factors of 10 that divides 10 without a remainder.

1, 2, 5, 10

Least Common Multiple of 27 and 10 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 10, than apply into the LCM equation.

GCF(27,10) = 1
LCM(27,10) = ( 27 × 10) / 1
LCM(27,10) = 270 / 1
LCM(27,10) = 270

Properties of LCM 27 and 10

(i) The LCM of 10 and 27 is associative

LCM of 27 and 10 = LCM of 10 and 27

Related Least Common Multiples of 27

Related Least Common Multiples of 10

Frequently Asked Questions on LCM of 27 and 10

1. What is the LCM of 27 and 10?

Answer: LCM of 27 and 10 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 10?

Answer: Factors of 10 are 1, 2, 5, 10. There are 4 integers that are factors of 10. The greatest factor of 10 is 10.

4. How to Find the LCM of 27 and 10?

Answer:

Least Common Multiple of 27 and 10 = 270

Step 1: Find the prime factorization of 27

27 = 3 x 3 x 3

Step 2: Find the prime factorization of 10

10 = 2 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 10 is 270.