Least Common Multiple of 128 and 135

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 128 and 135 the smallest integer that is 17280 that is divisible by both numbers.

Least Common Multiple (LCM) of 128 and 135 is 17280.

LCM(128,135) = 17280

LCM of 128 and 135

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

LCM of:
and

Least Common Multiple of 128 and 135

LCM of 128 and 135 is 17280

Least common multiple can be found by multiplying the highest exponent prime factors of 128 and 135. First we will calculate the prime factors of 128 and 135.

Prime Factorization of 128


2 128
2 64
2 32
2 16
2 8
2 4
2 2
1

Prime factors of 128 are 2. Prime factorization of 128 in exponential form is:

128 = 27

Prime Factorization of 135


3 135
3 45
3 15
5 5
1

Prime factors of 135 are 3,5. Prime factorization of 135 in exponential form is:

135 = 33×51

Now multiplying the highest exponent prime factors to calculate the LCM of 128 and 135.

LCM(128,135) = 27×33×51
LCM(128,135) = 17280

Factors of 128

List of positive integer factors of 128 that divides 128 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128

Factors of 135

List of positive integer factors of 135 that divides 135 without a remainder.

1, 3, 5, 9, 15, 27, 45, 135

Least Common Multiple of 128 and 135 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 128 and 135, than apply into the LCM equation.

GCF(128,135) = 1
LCM(128,135) = ( 128 × 135) / 1
LCM(128,135) = 17280 / 1
LCM(128,135) = 17280

Properties of LCM 128 and 135

(i) The LCM of 135 and 128 is associative

LCM of 128 and 135 = LCM of 135 and 128

Related Least Common Multiples of 128

Related Least Common Multiples of 135

Frequently Asked Questions on LCM of 128 and 135

1. What is the LCM of 128 and 135?

Answer: LCM of 128 and 135 is 17280.

2. What are the Factors of 128?

Answer: Factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128. There are 8 integers that are factors of 128. The greatest factor of 128 is 128.

3. What are the Factors of 135?

Answer: Factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135. There are 8 integers that are factors of 135. The greatest factor of 135 is 135.

4. How to Find the LCM of 128 and 135?

Answer:

Least Common Multiple of 128 and 135 = 17280

Step 1: Find the prime factorization of 128

128 = 2 x 2 x 2 x 2 x 2 x 2 x 2

Step 2: Find the prime factorization of 135

135 = 3 x 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 = 17280 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5

Step 4: Therefore, the least common multiple of 128 and 135 is 17280.