Least Common Multiple of 72 and 85

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 85 the smallest integer that is 6120 that is divisible by both numbers.

Least Common Multiple (LCM) of 72 and 85 is 6120.

LCM(72,85) = 6120

LCM of 72 and 85

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

LCM of:
and

Least Common Multiple of 72 and 85

LCM of 72 and 85 is 6120

Least common multiple can be found by multiplying the highest exponent prime factors of 72 and 85. First we will calculate the prime factors of 72 and 85.

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 85


5 85
17 17
1

Prime factors of 85 are 5,17. Prime factorization of 85 in exponential form is:

85 = 51×171

Now multiplying the highest exponent prime factors to calculate the LCM of 72 and 85.

LCM(72,85) = 23×32×51×171
LCM(72,85) = 6120

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 85

List of positive integer factors of 85 that divides 85 without a remainder.

1, 5, 17, 85

Least Common Multiple of 72 and 85 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 85, than apply into the LCM equation.

GCF(72,85) = 1
LCM(72,85) = ( 72 × 85) / 1
LCM(72,85) = 6120 / 1
LCM(72,85) = 6120

Properties of LCM 72 and 85

(i) The LCM of 85 and 72 is associative

LCM of 72 and 85 = LCM of 85 and 72

Related Least Common Multiples of 72

Related Least Common Multiples of 85

Frequently Asked Questions on LCM of 72 and 85

1. What is the LCM of 72 and 85?

Answer: LCM of 72 and 85 is 6120.

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 85?

Answer: Factors of 85 are 1, 5, 17, 85. There are 4 integers that are factors of 85. The greatest factor of 85 is 85.

4. How to Find the LCM of 72 and 85?

Answer:

Least Common Multiple of 72 and 85 = 6120

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 85

85 = 5 x 17

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 6120 = 2 x 2 x 2 x 3 x 3 x 5 x 17

Step 4: Therefore, the least common multiple of 72 and 85 is 6120.