Least Common Multiple of 54 and 67

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 67 the smallest integer that is 3618 that is divisible by both numbers.

Least Common Multiple (LCM) of 54 and 67 is 3618.

LCM(54,67) = 3618

LCM of 54 and 67

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

LCM of:
and

Least Common Multiple of 54 and 67

LCM of 54 and 67 is 3618

Least common multiple can be found by multiplying the highest exponent prime factors of 54 and 67. First we will calculate the prime factors of 54 and 67.

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 67


67 67
1

Prime factors of 67 are 67. Prime factorization of 67 in exponential form is:

67 = 671

Now multiplying the highest exponent prime factors to calculate the LCM of 54 and 67.

LCM(54,67) = 21×33×671
LCM(54,67) = 3618

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 67

List of positive integer factors of 67 that divides 67 without a remainder.

1, 67

Least Common Multiple of 54 and 67 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 67, than apply into the LCM equation.

GCF(54,67) = 1
LCM(54,67) = ( 54 × 67) / 1
LCM(54,67) = 3618 / 1
LCM(54,67) = 3618

Properties of LCM 54 and 67

(i) The LCM of 67 and 54 is associative

LCM of 54 and 67 = LCM of 67 and 54

Related Least Common Multiples of 54

Related Least Common Multiples of 67

Frequently Asked Questions on LCM of 54 and 67

1. What is the LCM of 54 and 67?

Answer: LCM of 54 and 67 is 3618.

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 67?

Answer: Factors of 67 are 1, 67. There are 2 integers that are factors of 67. The greatest factor of 67 is 67.

4. How to Find the LCM of 54 and 67?

Answer:

Least Common Multiple of 54 and 67 = 3618

Step 1: Find the prime factorization of 54

54 = 2 x 3 x 3 x 3

Step 2: Find the prime factorization of 67

67 = 67

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

LCM = 3618 = 2 x 3 x 3 x 3 x 67

Step 4: Therefore, the least common multiple of 54 and 67 is 3618.