Least Common Multiple of 45 and 63

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 63 the smallest integer that is 315 that is divisible by both numbers.

Least Common Multiple (LCM) of 45 and 63 is 315.

LCM(45,63) = 315

LCM of 45 and 63

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

LCM of:
and

Least Common Multiple of 45 and 63

LCM of 45 and 63 is 315

Least common multiple can be found by multiplying the highest exponent prime factors of 45 and 63. First we will calculate the prime factors of 45 and 63.

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 63


3 63
3 21
7 7
1

Prime factors of 63 are 3,7. Prime factorization of 63 in exponential form is:

63 = 32×71

Now multiplying the highest exponent prime factors to calculate the LCM of 45 and 63.

LCM(45,63) = 32×51×71
LCM(45,63) = 315

Factors of 45

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

1, 3, 5, 9, 15, 45

Factors of 63

List of positive integer factors of 63 that divides 63 without a remainder.

1, 3, 7, 9, 21, 63

Least Common Multiple of 45 and 63 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 63, than apply into the LCM equation.

GCF(45,63) = 9
LCM(45,63) = ( 45 × 63) / 9
LCM(45,63) = 2835 / 9
LCM(45,63) = 315

Properties of LCM 45 and 63

(i) The LCM of 63 and 45 is associative

LCM of 45 and 63 = LCM of 63 and 45

Related Least Common Multiples of 45

Related Least Common Multiples of 63

Frequently Asked Questions on LCM of 45 and 63

1. What is the LCM of 45 and 63?

Answer: LCM of 45 and 63 is 315.

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 63?

Answer: Factors of 63 are 1, 3, 7, 9, 21, 63. There are 6 integers that are factors of 63. The greatest factor of 63 is 63.

4. How to Find the LCM of 45 and 63?

Answer:

Least Common Multiple of 45 and 63 = 315

Step 1: Find the prime factorization of 45

45 = 3 x 3 x 5

Step 2: Find the prime factorization of 63

63 = 3 x 3 x 7

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

LCM = 315 = 3 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 45 and 63 is 315.