Least Common Multiple of 72 and 51

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 51 the smallest integer that is 1224 that is divisible by both numbers.

Least Common Multiple (LCM) of 72 and 51 is 1224.

LCM(72,51) = 1224

LCM of 72 and 51

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

LCM of:
and

Least Common Multiple of 72 and 51

LCM of 72 and 51 is 1224

Least common multiple can be found by multiplying the highest exponent prime factors of 72 and 51. First we will calculate the prime factors of 72 and 51.

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 51


3 51
17 17
1

Prime factors of 51 are 3,17. Prime factorization of 51 in exponential form is:

51 = 31×171

Now multiplying the highest exponent prime factors to calculate the LCM of 72 and 51.

LCM(72,51) = 23×32×171
LCM(72,51) = 1224

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 51

List of positive integer factors of 51 that divides 51 without a remainder.

1, 3, 17, 51

Least Common Multiple of 72 and 51 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 51, than apply into the LCM equation.

GCF(72,51) = 3
LCM(72,51) = ( 72 × 51) / 3
LCM(72,51) = 3672 / 3
LCM(72,51) = 1224

Properties of LCM 72 and 51

(i) The LCM of 51 and 72 is associative

LCM of 72 and 51 = LCM of 51 and 72

Related Least Common Multiples of 72

Related Least Common Multiples of 51

Frequently Asked Questions on LCM of 72 and 51

1. What is the LCM of 72 and 51?

Answer: LCM of 72 and 51 is 1224.

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 51?

Answer: Factors of 51 are 1, 3, 17, 51. There are 4 integers that are factors of 51. The greatest factor of 51 is 51.

4. How to Find the LCM of 72 and 51?

Answer:

Least Common Multiple of 72 and 51 = 1224

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 51

51 = 3 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 = 1224 = 2 x 2 x 2 x 3 x 3 x 17

Step 4: Therefore, the least common multiple of 72 and 51 is 1224.