Least Common Multiple of 72 and 74

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 74 the smallest integer that is 2664 that is divisible by both numbers.

Least Common Multiple (LCM) of 72 and 74 is 2664.

LCM(72,74) = 2664

LCM of 72 and 74

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

LCM of:
and

Least Common Multiple of 72 and 74

LCM of 72 and 74 is 2664

Least common multiple can be found by multiplying the highest exponent prime factors of 72 and 74. First we will calculate the prime factors of 72 and 74.

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 74


2 74
37 37
1

Prime factors of 74 are 2,37. Prime factorization of 74 in exponential form is:

74 = 21×371

Now multiplying the highest exponent prime factors to calculate the LCM of 72 and 74.

LCM(72,74) = 23×32×371
LCM(72,74) = 2664

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 74

List of positive integer factors of 74 that divides 74 without a remainder.

1, 2, 37, 74

Least Common Multiple of 72 and 74 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 74, than apply into the LCM equation.

GCF(72,74) = 2
LCM(72,74) = ( 72 × 74) / 2
LCM(72,74) = 5328 / 2
LCM(72,74) = 2664

Properties of LCM 72 and 74

(i) The LCM of 74 and 72 is associative

LCM of 72 and 74 = LCM of 74 and 72

Related Least Common Multiples of 72

Related Least Common Multiples of 74

Frequently Asked Questions on LCM of 72 and 74

1. What is the LCM of 72 and 74?

Answer: LCM of 72 and 74 is 2664.

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 74?

Answer: Factors of 74 are 1, 2, 37, 74. There are 4 integers that are factors of 74. The greatest factor of 74 is 74.

4. How to Find the LCM of 72 and 74?

Answer:

Least Common Multiple of 72 and 74 = 2664

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 74

74 = 2 x 37

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

LCM = 2664 = 2 x 2 x 2 x 3 x 3 x 37

Step 4: Therefore, the least common multiple of 72 and 74 is 2664.