Least Common Multiple of 45 and 53

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 53 the smallest integer that is 2385 that is divisible by both numbers.

Least Common Multiple (LCM) of 45 and 53 is 2385.

LCM(45,53) = 2385

LCM of 45 and 53

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

LCM of:
and

Least Common Multiple of 45 and 53

LCM of 45 and 53 is 2385

Least common multiple can be found by multiplying the highest exponent prime factors of 45 and 53. First we will calculate the prime factors of 45 and 53.

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 53


53 53
1

Prime factors of 53 are 53. Prime factorization of 53 in exponential form is:

53 = 531

Now multiplying the highest exponent prime factors to calculate the LCM of 45 and 53.

LCM(45,53) = 32×51×531
LCM(45,53) = 2385

Factors of 45

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

1, 3, 5, 9, 15, 45

Factors of 53

List of positive integer factors of 53 that divides 53 without a remainder.

1, 53

Least Common Multiple of 45 and 53 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 53, than apply into the LCM equation.

GCF(45,53) = 1
LCM(45,53) = ( 45 × 53) / 1
LCM(45,53) = 2385 / 1
LCM(45,53) = 2385

Properties of LCM 45 and 53

(i) The LCM of 53 and 45 is associative

LCM of 45 and 53 = LCM of 53 and 45

Related Least Common Multiples of 45

Related Least Common Multiples of 53

Frequently Asked Questions on LCM of 45 and 53

1. What is the LCM of 45 and 53?

Answer: LCM of 45 and 53 is 2385.

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 53?

Answer: Factors of 53 are 1, 53. There are 2 integers that are factors of 53. The greatest factor of 53 is 53.

4. How to Find the LCM of 45 and 53?

Answer:

Least Common Multiple of 45 and 53 = 2385

Step 1: Find the prime factorization of 45

45 = 3 x 3 x 5

Step 2: Find the prime factorization of 53

53 = 53

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

LCM = 2385 = 3 x 3 x 5 x 53

Step 4: Therefore, the least common multiple of 45 and 53 is 2385.