Least Common Multiple of 123 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 123 and 128 the smallest integer that is 15744 that is divisible by both numbers.

Least Common Multiple (LCM) of 123 and 128 is 15744.

LCM(123,128) = 15744

LCM of 123 and 128

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

LCM of:
and

Least Common Multiple of 123 and 128

LCM of 123 and 128 is 15744

Least common multiple can be found by multiplying the highest exponent prime factors of 123 and 128. First we will calculate the prime factors of 123 and 128.

Prime Factorization of 123


3 123
41 41
1

Prime factors of 123 are 3,41. Prime factorization of 123 in exponential form is:

123 = 31×411

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 123 and 128.

LCM(123,128) = 27×31×411
LCM(123,128) = 15744

Factors of 123

List of positive integer factors of 123 that divides 123 without a remainder.

1, 3, 41, 123

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 123 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 123 and 128, than apply into the LCM equation.

GCF(123,128) = 1
LCM(123,128) = ( 123 × 128) / 1
LCM(123,128) = 15744 / 1
LCM(123,128) = 15744

Properties of LCM 123 and 128

(i) The LCM of 128 and 123 is associative

LCM of 123 and 128 = LCM of 128 and 123

Related Least Common Multiples of 123

Related Least Common Multiples of 128

Frequently Asked Questions on LCM of 123 and 128

1. What is the LCM of 123 and 128?

Answer: LCM of 123 and 128 is 15744.

2. What are the Factors of 123?

Answer: Factors of 123 are 1, 3, 41, 123. There are 4 integers that are factors of 123. The greatest factor of 123 is 123.

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 123 and 128?

Answer:

Least Common Multiple of 123 and 128 = 15744

Step 1: Find the prime factorization of 123

123 = 3 x 41

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 = 15744 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 41

Step 4: Therefore, the least common multiple of 123 and 128 is 15744.