Least Common Multiple of 72 and 80

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 72 and 80 the smallest integer that is 720 that is divisible by both numbers.

Least Common Multiple (LCM) of 72 and 80 is 720.

LCM(72,80) = 720

LCM of 72 and 80

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

LCM of:
and

Least Common Multiple of 72 and 80

LCM of 72 and 80 is 720

Least common multiple can be found by multiplying the highest exponent prime factors of 72 and 80. First we will calculate the prime factors of 72 and 80.

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

Prime Factorization of 80


2 80
2 40
2 20
2 10
5 5
1

Prime factors of 80 are 2,5. Prime factorization of 80 in exponential form is:

80 = 24×51

Now multiplying the highest exponent prime factors to calculate the LCM of 72 and 80.

LCM(72,80) = 24×32×51
LCM(72,80) = 720

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

Factors of 80

List of positive integer factors of 80 that divides 80 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80

Least Common Multiple of 72 and 80 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72 and 80, than apply into the LCM equation.

GCF(72,80) = 8
LCM(72,80) = ( 72 × 80) / 8
LCM(72,80) = 5760 / 8
LCM(72,80) = 720

Properties of LCM 72 and 80

(i) The LCM of 80 and 72 is associative

LCM of 72 and 80 = LCM of 80 and 72

Related Least Common Multiples of 72

Related Least Common Multiples of 80

Frequently Asked Questions on LCM of 72 and 80

1. What is the LCM of 72 and 80?

Answer: LCM of 72 and 80 is 720.

2. 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.

3. What are the Factors of 80?

Answer: Factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80. There are 10 integers that are factors of 80. The greatest factor of 80 is 80.

4. How to Find the LCM of 72 and 80?

Answer:

Least Common Multiple of 72 and 80 = 720

Step 1: Find the prime factorization of 72

72 = 2 x 2 x 2 x 3 x 3

Step 2: Find the prime factorization of 80

80 = 2 x 2 x 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 = 720 = 2 x 2 x 2 x 2 x 3 x 3 x 5

Step 4: Therefore, the least common multiple of 72 and 80 is 720.