Least Common Multiple of 54 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 54 and 74 the smallest integer that is 1998 that is divisible by both numbers.

Least Common Multiple (LCM) of 54 and 74 is 1998.

LCM(54,74) = 1998

LCM of 54 and 74

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

LCM of:
and

Least Common Multiple of 54 and 74

LCM of 54 and 74 is 1998

Least common multiple can be found by multiplying the highest exponent prime factors of 54 and 74. First we will calculate the prime factors of 54 and 74.

Prime Factorization of 54


2 54
3 27
3 9
3 3
1

Prime factors of 54 are 2,3. Prime factorization of 54 in exponential form is:

54 = 21×33

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 54 and 74.

LCM(54,74) = 21×33×371
LCM(54,74) = 1998

Factors of 54

List of positive integer factors of 54 that divides 54 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54

Factors of 74

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

1, 2, 37, 74

Least Common Multiple of 54 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 54 and 74, than apply into the LCM equation.

GCF(54,74) = 2
LCM(54,74) = ( 54 × 74) / 2
LCM(54,74) = 3996 / 2
LCM(54,74) = 1998

Properties of LCM 54 and 74

(i) The LCM of 74 and 54 is associative

LCM of 54 and 74 = LCM of 74 and 54

Related Least Common Multiples of 54

Related Least Common Multiples of 74

Frequently Asked Questions on LCM of 54 and 74

1. What is the LCM of 54 and 74?

Answer: LCM of 54 and 74 is 1998.

2. What are the Factors of 54?

Answer: Factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54. There are 8 integers that are factors of 54. The greatest factor of 54 is 54.

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 54 and 74?

Answer:

Least Common Multiple of 54 and 74 = 1998

Step 1: Find the prime factorization of 54

54 = 2 x 3 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 = 1998 = 2 x 3 x 3 x 3 x 37

Step 4: Therefore, the least common multiple of 54 and 74 is 1998.