Least Common Multiple of 18 and 20

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 18 and 20 the smallest integer that is 180 that is divisible by both numbers.

Least Common Multiple (LCM) of 18 and 20 is 180.

LCM(18,20) = 180

LCM of 18 and 20

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

LCM of:
and

Least Common Multiple of 18 and 20

LCM of 18 and 20 is 180

Least common multiple can be found by multiplying the highest exponent prime factors of 18 and 20. First we will calculate the prime factors of 18 and 20.

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

Prime Factorization of 20


2 20
2 10
5 5
1

Prime factors of 20 are 2,5. Prime factorization of 20 in exponential form is:

20 = 22×51

Now multiplying the highest exponent prime factors to calculate the LCM of 18 and 20.

LCM(18,20) = 22×32×51
LCM(18,20) = 180

Factors of 18

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

1, 2, 3, 6, 9, 18

Factors of 20

List of positive integer factors of 20 that divides 20 without a remainder.

1, 2, 4, 5, 10, 20

Least Common Multiple of 18 and 20 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 18 and 20, than apply into the LCM equation.

GCF(18,20) = 2
LCM(18,20) = ( 18 × 20) / 2
LCM(18,20) = 360 / 2
LCM(18,20) = 180

Properties of LCM 18 and 20

(i) The LCM of 20 and 18 is associative

LCM of 18 and 20 = LCM of 20 and 18

Related Least Common Multiples of 18

Related Least Common Multiples of 20

Frequently Asked Questions on LCM of 18 and 20

1. What is the LCM of 18 and 20?

Answer: LCM of 18 and 20 is 180.

2. 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.

3. What are the Factors of 20?

Answer: Factors of 20 are 1, 2, 4, 5, 10, 20. There are 6 integers that are factors of 20. The greatest factor of 20 is 20.

4. How to Find the LCM of 18 and 20?

Answer:

Least Common Multiple of 18 and 20 = 180

Step 1: Find the prime factorization of 18

18 = 2 x 3 x 3

Step 2: Find the prime factorization of 20

20 = 2 x 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 = 180 = 2 x 2 x 3 x 3 x 5

Step 4: Therefore, the least common multiple of 18 and 20 is 180.