Least Common Multiple of 45 and 48

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 48 the smallest integer that is 720 that is divisible by both numbers.

Least Common Multiple (LCM) of 45 and 48 is 720.

LCM(45,48) = 720

LCM of 45 and 48

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

LCM of:
and

Least Common Multiple of 45 and 48

LCM of 45 and 48 is 720

Least common multiple can be found by multiplying the highest exponent prime factors of 45 and 48. First we will calculate the prime factors of 45 and 48.

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 48


2 48
2 24
2 12
2 6
3 3
1

Prime factors of 48 are 2,3. Prime factorization of 48 in exponential form is:

48 = 24×31

Now multiplying the highest exponent prime factors to calculate the LCM of 45 and 48.

LCM(45,48) = 24×32×51
LCM(45,48) = 720

Factors of 45

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

1, 3, 5, 9, 15, 45

Factors of 48

List of positive integer factors of 48 that divides 48 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Least Common Multiple of 45 and 48 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 48, than apply into the LCM equation.

GCF(45,48) = 3
LCM(45,48) = ( 45 × 48) / 3
LCM(45,48) = 2160 / 3
LCM(45,48) = 720

Properties of LCM 45 and 48

(i) The LCM of 48 and 45 is associative

LCM of 45 and 48 = LCM of 48 and 45

Related Least Common Multiples of 45

Related Least Common Multiples of 48

Frequently Asked Questions on LCM of 45 and 48

1. What is the LCM of 45 and 48?

Answer: LCM of 45 and 48 is 720.

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 48?

Answer: Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. There are 10 integers that are factors of 48. The greatest factor of 48 is 48.

4. How to Find the LCM of 45 and 48?

Answer:

Least Common Multiple of 45 and 48 = 720

Step 1: Find the prime factorization of 45

45 = 3 x 3 x 5

Step 2: Find the prime factorization of 48

48 = 2 x 2 x 2 x 2 x 3

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

LCM = 720 = 2 x 2 x 2 x 2 x 3 x 3 x 5

Step 4: Therefore, the least common multiple of 45 and 48 is 720.