Least Common Multiple of 45 and 57

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 57 the smallest integer that is 855 that is divisible by both numbers.

Least Common Multiple (LCM) of 45 and 57 is 855.

LCM(45,57) = 855

LCM of 45 and 57

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

LCM of:
and

Least Common Multiple of 45 and 57

LCM of 45 and 57 is 855

Least common multiple can be found by multiplying the highest exponent prime factors of 45 and 57. First we will calculate the prime factors of 45 and 57.

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 57


3 57
19 19
1

Prime factors of 57 are 3,19. Prime factorization of 57 in exponential form is:

57 = 31×191

Now multiplying the highest exponent prime factors to calculate the LCM of 45 and 57.

LCM(45,57) = 32×51×191
LCM(45,57) = 855

Factors of 45

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

1, 3, 5, 9, 15, 45

Factors of 57

List of positive integer factors of 57 that divides 57 without a remainder.

1, 3, 19, 57

Least Common Multiple of 45 and 57 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 57, than apply into the LCM equation.

GCF(45,57) = 3
LCM(45,57) = ( 45 × 57) / 3
LCM(45,57) = 2565 / 3
LCM(45,57) = 855

Properties of LCM 45 and 57

(i) The LCM of 57 and 45 is associative

LCM of 45 and 57 = LCM of 57 and 45

Related Least Common Multiples of 45

Related Least Common Multiples of 57

Frequently Asked Questions on LCM of 45 and 57

1. What is the LCM of 45 and 57?

Answer: LCM of 45 and 57 is 855.

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 57?

Answer: Factors of 57 are 1, 3, 19, 57. There are 4 integers that are factors of 57. The greatest factor of 57 is 57.

4. How to Find the LCM of 45 and 57?

Answer:

Least Common Multiple of 45 and 57 = 855

Step 1: Find the prime factorization of 45

45 = 3 x 3 x 5

Step 2: Find the prime factorization of 57

57 = 3 x 19

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

LCM = 855 = 3 x 3 x 5 x 19

Step 4: Therefore, the least common multiple of 45 and 57 is 855.