Least Common Multiple of 54 and 65

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 65 the smallest integer that is 3510 that is divisible by both numbers.

Least Common Multiple (LCM) of 54 and 65 is 3510.

LCM(54,65) = 3510

LCM of 54 and 65

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

LCM of:
and

Least Common Multiple of 54 and 65

LCM of 54 and 65 is 3510

Least common multiple can be found by multiplying the highest exponent prime factors of 54 and 65. First we will calculate the prime factors of 54 and 65.

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 65


5 65
13 13
1

Prime factors of 65 are 5,13. Prime factorization of 65 in exponential form is:

65 = 51×131

Now multiplying the highest exponent prime factors to calculate the LCM of 54 and 65.

LCM(54,65) = 21×33×51×131
LCM(54,65) = 3510

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 65

List of positive integer factors of 65 that divides 65 without a remainder.

1, 5, 13, 65

Least Common Multiple of 54 and 65 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 65, than apply into the LCM equation.

GCF(54,65) = 1
LCM(54,65) = ( 54 × 65) / 1
LCM(54,65) = 3510 / 1
LCM(54,65) = 3510

Properties of LCM 54 and 65

(i) The LCM of 65 and 54 is associative

LCM of 54 and 65 = LCM of 65 and 54

Related Least Common Multiples of 54

Related Least Common Multiples of 65

Frequently Asked Questions on LCM of 54 and 65

1. What is the LCM of 54 and 65?

Answer: LCM of 54 and 65 is 3510.

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 65?

Answer: Factors of 65 are 1, 5, 13, 65. There are 4 integers that are factors of 65. The greatest factor of 65 is 65.

4. How to Find the LCM of 54 and 65?

Answer:

Least Common Multiple of 54 and 65 = 3510

Step 1: Find the prime factorization of 54

54 = 2 x 3 x 3 x 3

Step 2: Find the prime factorization of 65

65 = 5 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 = 3510 = 2 x 3 x 3 x 3 x 5 x 13

Step 4: Therefore, the least common multiple of 54 and 65 is 3510.