Least Common Multiple of 42 and 54

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023


Free LCM Calculator determines the least common multiple (LCM) between 42 and 54 the smallest integer that is 378 that is divisible by both numbers.

Least Common Multiple (LCM) of 42 and 54 is 378.

LCM(42,54) = 378

LCM of 42 and 54

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

LCM of:
and

Least Common Multiple of 42 and 54

LCM of 42 and 54 is 378

Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 54. First we will calculate the prime factors of 42 and 54.

Prime Factorization of 42


2 42
3 21
7 7
1

Prime factors of 42 are 2, 3,7. Prime factorization of 42 in exponential form is:

42 = 21×31×71

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

Now multiplying the highest exponent prime factors to calculate the LCM of 42 and 54.

LCM(42,54) = 21×33×71
LCM(42,54) = 378

Factors of 42

List of positive integer factors of 42 that divides 42 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42

Factors of 54

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

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

Least Common Multiple of 42 and 54 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42 and 54, than apply into the LCM equation.

GCF(42,54) = 6
LCM(42,54) = ( 42 × 54) / 6
LCM(42,54) = 2268 / 6
LCM(42,54) = 378

Properties of LCM 42 and 54

(i) The LCM of 54 and 42 is associative

LCM of 42 and 54 = LCM of 54 and 42

Frequently Asked Questions on LCM of 42 and 54

1. What is the LCM of 42 and 54?

Answer: LCM of 42 and 54 is 378.

2. What are the Factors of 42?

Answer: Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. There are 8 integers that are factors of 42. The greatest factor of 42 is 42.

3. 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.

4. How to Find the LCM of 42 and 54?

Answer:

Least Common Multiple of 42 and 54 = 378

Step 1: Find the prime factorization of 42

42 = 2 x 3 x 7

Step 2: Find the prime factorization of 54

54 = 2 x 3 x 3 x 3

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

LCM = 378 = 2 x 3 x 3 x 3 x 7

Step 4: Therefore, the least common multiple of 42 and 54 is 378.