Least Common Multiple of 49 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 49 and 54 the smallest integer that is 2646 that is divisible by both numbers.

Least Common Multiple (LCM) of 49 and 54 is 2646.

LCM(49,54) = 2646

LCM of 49 and 54

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

LCM of:
and

Least Common Multiple of 49 and 54

LCM of 49 and 54 is 2646

Least common multiple can be found by multiplying the highest exponent prime factors of 49 and 54. First we will calculate the prime factors of 49 and 54.

Prime Factorization of 49


7 49
7 7
1

Prime factors of 49 are 7. Prime factorization of 49 in exponential form is:

49 = 72

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 49 and 54.

LCM(49,54) = 21×33×72
LCM(49,54) = 2646

Factors of 49

List of positive integer factors of 49 that divides 49 without a remainder.

1, 7, 49

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 49 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 49 and 54, than apply into the LCM equation.

GCF(49,54) = 1
LCM(49,54) = ( 49 × 54) / 1
LCM(49,54) = 2646 / 1
LCM(49,54) = 2646

Properties of LCM 49 and 54

(i) The LCM of 54 and 49 is associative

LCM of 49 and 54 = LCM of 54 and 49

Related Least Common Multiples of 49

Related Least Common Multiples of 54

Frequently Asked Questions on LCM of 49 and 54

1. What is the LCM of 49 and 54?

Answer: LCM of 49 and 54 is 2646.

2. What are the Factors of 49?

Answer: Factors of 49 are 1, 7, 49. There are 3 integers that are factors of 49. The greatest factor of 49 is 49.

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 49 and 54?

Answer:

Least Common Multiple of 49 and 54 = 2646

Step 1: Find the prime factorization of 49

49 = 7 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 = 2646 = 2 x 3 x 3 x 3 x 7 x 7

Step 4: Therefore, the least common multiple of 49 and 54 is 2646.