Least Common Multiple of 45 and 56

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 45 and 56 the smallest integer that is 2520 that is divisible by both numbers.

Least Common Multiple (LCM) of 45 and 56 is 2520.

LCM(45,56) = 2520

LCM of 45 and 56

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

LCM of:
and

Least Common Multiple of 45 and 56

LCM of 45 and 56 is 2520

Least common multiple can be found by multiplying the highest exponent prime factors of 45 and 56. First we will calculate the prime factors of 45 and 56.

Prime Factorization of 45


3 45
3 15
5 5
1

Prime factors of 45 are 3,5. Prime factorization of 45 in exponential form is:

45 = 32×51

Prime Factorization of 56


2 56
2 28
2 14
7 7
1

Prime factors of 56 are 2,7. Prime factorization of 56 in exponential form is:

56 = 23×71

Now multiplying the highest exponent prime factors to calculate the LCM of 45 and 56.

LCM(45,56) = 23×32×51×71
LCM(45,56) = 2520

Factors of 45

List of positive integer factors of 45 that divides 45 without a remainder.

1, 3, 5, 9, 15, 45

Factors of 56

List of positive integer factors of 56 that divides 56 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56

Least Common Multiple of 45 and 56 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45 and 56, than apply into the LCM equation.

GCF(45,56) = 1
LCM(45,56) = ( 45 × 56) / 1
LCM(45,56) = 2520 / 1
LCM(45,56) = 2520

Properties of LCM 45 and 56

(i) The LCM of 56 and 45 is associative

LCM of 45 and 56 = LCM of 56 and 45

Related Least Common Multiples of 45

Related Least Common Multiples of 56

Frequently Asked Questions on LCM of 45 and 56

1. What is the LCM of 45 and 56?

Answer: LCM of 45 and 56 is 2520.

2. What are the Factors of 45?

Answer: Factors of 45 are 1, 3, 5, 9, 15, 45. There are 6 integers that are factors of 45. The greatest factor of 45 is 45.

3. What are the Factors of 56?

Answer: Factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56. There are 8 integers that are factors of 56. The greatest factor of 56 is 56.

4. How to Find the LCM of 45 and 56?

Answer:

Least Common Multiple of 45 and 56 = 2520

Step 1: Find the prime factorization of 45

45 = 3 x 3 x 5

Step 2: Find the prime factorization of 56

56 = 2 x 2 x 2 x 7

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

LCM = 2520 = 2 x 2 x 2 x 3 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 45 and 56 is 2520.