Least Common Multiple of 45 and 52

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 52 the smallest integer that is 2340 that is divisible by both numbers.

Least Common Multiple (LCM) of 45 and 52 is 2340.

LCM(45,52) = 2340

LCM of 45 and 52

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

LCM of:
and

Least Common Multiple of 45 and 52

LCM of 45 and 52 is 2340

Least common multiple can be found by multiplying the highest exponent prime factors of 45 and 52. First we will calculate the prime factors of 45 and 52.

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 52


2 52
2 26
13 13
1

Prime factors of 52 are 2,13. Prime factorization of 52 in exponential form is:

52 = 22×131

Now multiplying the highest exponent prime factors to calculate the LCM of 45 and 52.

LCM(45,52) = 22×32×51×131
LCM(45,52) = 2340

Factors of 45

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

1, 3, 5, 9, 15, 45

Factors of 52

List of positive integer factors of 52 that divides 52 without a remainder.

1, 2, 4, 13, 26, 52

Least Common Multiple of 45 and 52 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 52, than apply into the LCM equation.

GCF(45,52) = 1
LCM(45,52) = ( 45 × 52) / 1
LCM(45,52) = 2340 / 1
LCM(45,52) = 2340

Properties of LCM 45 and 52

(i) The LCM of 52 and 45 is associative

LCM of 45 and 52 = LCM of 52 and 45

Related Least Common Multiples of 45

Related Least Common Multiples of 52

Frequently Asked Questions on LCM of 45 and 52

1. What is the LCM of 45 and 52?

Answer: LCM of 45 and 52 is 2340.

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 52?

Answer: Factors of 52 are 1, 2, 4, 13, 26, 52. There are 6 integers that are factors of 52. The greatest factor of 52 is 52.

4. How to Find the LCM of 45 and 52?

Answer:

Least Common Multiple of 45 and 52 = 2340

Step 1: Find the prime factorization of 45

45 = 3 x 3 x 5

Step 2: Find the prime factorization of 52

52 = 2 x 2 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 = 2340 = 2 x 2 x 3 x 3 x 5 x 13

Step 4: Therefore, the least common multiple of 45 and 52 is 2340.