Least Common Multiple of 120 and 128

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 120 and 128 the smallest integer that is 1920 that is divisible by both numbers.

Least Common Multiple (LCM) of 120 and 128 is 1920.

LCM(120,128) = 1920

LCM of 120 and 128

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

LCM of:
and

Least Common Multiple of 120 and 128

LCM of 120 and 128 is 1920

Least common multiple can be found by multiplying the highest exponent prime factors of 120 and 128. First we will calculate the prime factors of 120 and 128.

Prime Factorization of 120


2 120
2 60
2 30
3 15
5 5
1

Prime factors of 120 are 2, 3,5. Prime factorization of 120 in exponential form is:

120 = 23×31×51

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

Now multiplying the highest exponent prime factors to calculate the LCM of 120 and 128.

LCM(120,128) = 27×31×51
LCM(120,128) = 1920

Factors of 120

List of positive integer factors of 120 that divides 120 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Factors of 128

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

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

Least Common Multiple of 120 and 128 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 120 and 128, than apply into the LCM equation.

GCF(120,128) = 8
LCM(120,128) = ( 120 × 128) / 8
LCM(120,128) = 15360 / 8
LCM(120,128) = 1920

Properties of LCM 120 and 128

(i) The LCM of 128 and 120 is associative

LCM of 120 and 128 = LCM of 128 and 120

Related Least Common Multiples of 120

Related Least Common Multiples of 128

Frequently Asked Questions on LCM of 120 and 128

1. What is the LCM of 120 and 128?

Answer: LCM of 120 and 128 is 1920.

2. What are the Factors of 120?

Answer: Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. There are 16 integers that are factors of 120. The greatest factor of 120 is 120.

3. 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.

4. How to Find the LCM of 120 and 128?

Answer:

Least Common Multiple of 120 and 128 = 1920

Step 1: Find the prime factorization of 120

120 = 2 x 2 x 2 x 3 x 5

Step 2: Find the prime factorization of 128

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

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

LCM = 1920 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5

Step 4: Therefore, the least common multiple of 120 and 128 is 1920.