Least Common Multiple of 40 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 40 and 54 the smallest integer that is 1080 that is divisible by both numbers.

Least Common Multiple (LCM) of 40 and 54 is 1080.

LCM(40,54) = 1080

LCM of 40 and 54

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

LCM of:
and

Least Common Multiple of 40 and 54

LCM of 40 and 54 is 1080

Least common multiple can be found by multiplying the highest exponent prime factors of 40 and 54. First we will calculate the prime factors of 40 and 54.

Prime Factorization of 40


2 40
2 20
2 10
5 5
1

Prime factors of 40 are 2,5. Prime factorization of 40 in exponential form is:

40 = 23×51

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 40 and 54.

LCM(40,54) = 23×33×51
LCM(40,54) = 1080

Factors of 40

List of positive integer factors of 40 that divides 40 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40

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 40 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 40 and 54, than apply into the LCM equation.

GCF(40,54) = 2
LCM(40,54) = ( 40 × 54) / 2
LCM(40,54) = 2160 / 2
LCM(40,54) = 1080

Properties of LCM 40 and 54

(i) The LCM of 54 and 40 is associative

LCM of 40 and 54 = LCM of 54 and 40

Related Least Common Multiples of 40

Related Least Common Multiples of 54

Frequently Asked Questions on LCM of 40 and 54

1. What is the LCM of 40 and 54?

Answer: LCM of 40 and 54 is 1080.

2. What are the Factors of 40?

Answer: Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. There are 8 integers that are factors of 40. The greatest factor of 40 is 40.

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 40 and 54?

Answer:

Least Common Multiple of 40 and 54 = 1080

Step 1: Find the prime factorization of 40

40 = 2 x 2 x 2 x 5

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 = 1080 = 2 x 2 x 2 x 3 x 3 x 3 x 5

Step 4: Therefore, the least common multiple of 40 and 54 is 1080.