Least Common Multiple of 18 and 72

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 72 the smallest integer that is 72 that is divisible by both numbers.

Least Common Multiple (LCM) of 18 and 72 is 72.

LCM(18,72) = 72

LCM of 18 and 72

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

LCM of:
and

Least Common Multiple of 18 and 72

LCM of 18 and 72 is 72

Least common multiple can be found by multiplying the highest exponent prime factors of 18 and 72. First we will calculate the prime factors of 18 and 72.

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 72


2 72
2 36
2 18
3 9
3 3
1

Prime factors of 72 are 2,3. Prime factorization of 72 in exponential form is:

72 = 23×32

Now multiplying the highest exponent prime factors to calculate the LCM of 18 and 72.

LCM(18,72) = 23×32
LCM(18,72) = 72

Factors of 18

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

1, 2, 3, 6, 9, 18

Factors of 72

List of positive integer factors of 72 that divides 72 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Least Common Multiple of 18 and 72 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 72, than apply into the LCM equation.

GCF(18,72) = 18
LCM(18,72) = ( 18 × 72) / 18
LCM(18,72) = 1296 / 18
LCM(18,72) = 72

Properties of LCM 18 and 72

(i) The LCM of 72 and 18 is associative

LCM of 18 and 72 = LCM of 72 and 18

Related Least Common Multiples of 18

Related Least Common Multiples of 72

Frequently Asked Questions on LCM of 18 and 72

1. What is the LCM of 18 and 72?

Answer: LCM of 18 and 72 is 72.

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 72?

Answer: Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. There are 12 integers that are factors of 72. The greatest factor of 72 is 72.

4. How to Find the LCM of 18 and 72?

Answer:

Least Common Multiple of 18 and 72 = 72

Step 1: Find the prime factorization of 18

18 = 2 x 3 x 3

Step 2: Find the prime factorization of 72

72 = 2 x 2 x 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 = 72 = 2 x 2 x 2 x 3 x 3

Step 4: Therefore, the least common multiple of 18 and 72 is 72.