Least Common Multiple of 39 and 45

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 39 and 45 the smallest integer that is 585 that is divisible by both numbers.

Least Common Multiple (LCM) of 39 and 45 is 585.

LCM(39,45) = 585

LCM of 39 and 45

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

LCM of:
and

Least Common Multiple of 39 and 45

LCM of 39 and 45 is 585

Least common multiple can be found by multiplying the highest exponent prime factors of 39 and 45. First we will calculate the prime factors of 39 and 45.

Prime Factorization of 39


3 39
13 13
1

Prime factors of 39 are 3,13. Prime factorization of 39 in exponential form is:

39 = 31×131

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

Now multiplying the highest exponent prime factors to calculate the LCM of 39 and 45.

LCM(39,45) = 32×51×131
LCM(39,45) = 585

Factors of 39

List of positive integer factors of 39 that divides 39 without a remainder.

1, 3, 13, 39

Factors of 45

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

1, 3, 5, 9, 15, 45

Least Common Multiple of 39 and 45 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39 and 45, than apply into the LCM equation.

GCF(39,45) = 3
LCM(39,45) = ( 39 × 45) / 3
LCM(39,45) = 1755 / 3
LCM(39,45) = 585

Properties of LCM 39 and 45

(i) The LCM of 45 and 39 is associative

LCM of 39 and 45 = LCM of 45 and 39

Related Least Common Multiples of 39

Related Least Common Multiples of 45

Frequently Asked Questions on LCM of 39 and 45

1. What is the LCM of 39 and 45?

Answer: LCM of 39 and 45 is 585.

2. What are the Factors of 39?

Answer: Factors of 39 are 1, 3, 13, 39. There are 4 integers that are factors of 39. The greatest factor of 39 is 39.

3. 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.

4. How to Find the LCM of 39 and 45?

Answer:

Least Common Multiple of 39 and 45 = 585

Step 1: Find the prime factorization of 39

39 = 3 x 13

Step 2: Find the prime factorization of 45

45 = 3 x 3 x 5

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

LCM = 585 = 3 x 3 x 5 x 13

Step 4: Therefore, the least common multiple of 39 and 45 is 585.