Least Common Multiple of 45 and 51

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 51 the smallest integer that is 765 that is divisible by both numbers.

Least Common Multiple (LCM) of 45 and 51 is 765.

LCM(45,51) = 765

LCM of 45 and 51

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

LCM of:
and

Least Common Multiple of 45 and 51

LCM of 45 and 51 is 765

Least common multiple can be found by multiplying the highest exponent prime factors of 45 and 51. First we will calculate the prime factors of 45 and 51.

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 51


3 51
17 17
1

Prime factors of 51 are 3,17. Prime factorization of 51 in exponential form is:

51 = 31×171

Now multiplying the highest exponent prime factors to calculate the LCM of 45 and 51.

LCM(45,51) = 32×51×171
LCM(45,51) = 765

Factors of 45

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

1, 3, 5, 9, 15, 45

Factors of 51

List of positive integer factors of 51 that divides 51 without a remainder.

1, 3, 17, 51

Least Common Multiple of 45 and 51 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 51, than apply into the LCM equation.

GCF(45,51) = 3
LCM(45,51) = ( 45 × 51) / 3
LCM(45,51) = 2295 / 3
LCM(45,51) = 765

Properties of LCM 45 and 51

(i) The LCM of 51 and 45 is associative

LCM of 45 and 51 = LCM of 51 and 45

Related Least Common Multiples of 45

Related Least Common Multiples of 51

Frequently Asked Questions on LCM of 45 and 51

1. What is the LCM of 45 and 51?

Answer: LCM of 45 and 51 is 765.

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 51?

Answer: Factors of 51 are 1, 3, 17, 51. There are 4 integers that are factors of 51. The greatest factor of 51 is 51.

4. How to Find the LCM of 45 and 51?

Answer:

Least Common Multiple of 45 and 51 = 765

Step 1: Find the prime factorization of 45

45 = 3 x 3 x 5

Step 2: Find the prime factorization of 51

51 = 3 x 17

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

LCM = 765 = 3 x 3 x 5 x 17

Step 4: Therefore, the least common multiple of 45 and 51 is 765.