Least Common Multiple of 72 and 78

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 78 the smallest integer that is 936 that is divisible by both numbers.

Least Common Multiple (LCM) of 72 and 78 is 936.

LCM(72,78) = 936

LCM of 72 and 78

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

LCM of:
and

Least Common Multiple of 72 and 78

LCM of 72 and 78 is 936

Least common multiple can be found by multiplying the highest exponent prime factors of 72 and 78. First we will calculate the prime factors of 72 and 78.

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 78


2 78
3 39
13 13
1

Prime factors of 78 are 2, 3,13. Prime factorization of 78 in exponential form is:

78 = 21×31×131

Now multiplying the highest exponent prime factors to calculate the LCM of 72 and 78.

LCM(72,78) = 23×32×131
LCM(72,78) = 936

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 78

List of positive integer factors of 78 that divides 78 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78

Least Common Multiple of 72 and 78 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 78, than apply into the LCM equation.

GCF(72,78) = 6
LCM(72,78) = ( 72 × 78) / 6
LCM(72,78) = 5616 / 6
LCM(72,78) = 936

Properties of LCM 72 and 78

(i) The LCM of 78 and 72 is associative

LCM of 72 and 78 = LCM of 78 and 72

Related Least Common Multiples of 72

Related Least Common Multiples of 78

Frequently Asked Questions on LCM of 72 and 78

1. What is the LCM of 72 and 78?

Answer: LCM of 72 and 78 is 936.

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 78?

Answer: Factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78. There are 8 integers that are factors of 78. The greatest factor of 78 is 78.

4. How to Find the LCM of 72 and 78?

Answer:

Least Common Multiple of 72 and 78 = 936

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 78

78 = 2 x 3 x 13

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

LCM = 936 = 2 x 2 x 2 x 3 x 3 x 13

Step 4: Therefore, the least common multiple of 72 and 78 is 936.