Least Common Multiple of 15 and 18

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 15 and 18 the smallest integer that is 90 that is divisible by both numbers.

Least Common Multiple (LCM) of 15 and 18 is 90.

LCM(15,18) = 90

LCM of 15 and 18

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

LCM of:
and

Least Common Multiple of 15 and 18

LCM of 15 and 18 is 90

Least common multiple can be found by multiplying the highest exponent prime factors of 15 and 18. First we will calculate the prime factors of 15 and 18.

Prime Factorization of 15


3 15
5 5
1

Prime factors of 15 are 3,5. Prime factorization of 15 in exponential form is:

15 = 31×51

Prime Factorization of 18


2 18
3 9
3 3
1

Prime factors of 18 are 2,3. Prime factorization of 18 in exponential form is:

18 = 21×32

Now multiplying the highest exponent prime factors to calculate the LCM of 15 and 18.

LCM(15,18) = 21×32×51
LCM(15,18) = 90

Factors of 15

List of positive integer factors of 15 that divides 15 without a remainder.

1, 3, 5, 15

Factors of 18

List of positive integer factors of 18 that divides 18 without a remainder.

1, 2, 3, 6, 9, 18

Least Common Multiple of 15 and 18 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15 and 18, than apply into the LCM equation.

GCF(15,18) = 3
LCM(15,18) = ( 15 × 18) / 3
LCM(15,18) = 270 / 3
LCM(15,18) = 90

Properties of LCM 15 and 18

(i) The LCM of 18 and 15 is associative

LCM of 15 and 18 = LCM of 18 and 15

Related Least Common Multiples of 15

Related Least Common Multiples of 18

Frequently Asked Questions on LCM of 15 and 18

1. What is the LCM of 15 and 18?

Answer: LCM of 15 and 18 is 90.

2. What are the Factors of 15?

Answer: Factors of 15 are 1, 3, 5, 15. There are 4 integers that are factors of 15. The greatest factor of 15 is 15.

3. What are the Factors of 18?

Answer: Factors of 18 are 1, 2, 3, 6, 9, 18. There are 6 integers that are factors of 18. The greatest factor of 18 is 18.

4. How to Find the LCM of 15 and 18?

Answer:

Least Common Multiple of 15 and 18 = 90

Step 1: Find the prime factorization of 15

15 = 3 x 5

Step 2: Find the prime factorization of 18

18 = 2 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 = 90 = 2 x 3 x 3 x 5

Step 4: Therefore, the least common multiple of 15 and 18 is 90.