Least Common Multiple of 120 and 123

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 123 the smallest integer that is 4920 that is divisible by both numbers.

Least Common Multiple (LCM) of 120 and 123 is 4920.

LCM(120,123) = 4920

LCM of 120 and 123

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

LCM of:
and

Least Common Multiple of 120 and 123

LCM of 120 and 123 is 4920

Least common multiple can be found by multiplying the highest exponent prime factors of 120 and 123. First we will calculate the prime factors of 120 and 123.

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 123


3 123
41 41
1

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

123 = 31×411

Now multiplying the highest exponent prime factors to calculate the LCM of 120 and 123.

LCM(120,123) = 23×31×51×411
LCM(120,123) = 4920

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 123

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

1, 3, 41, 123

Least Common Multiple of 120 and 123 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 123, than apply into the LCM equation.

GCF(120,123) = 3
LCM(120,123) = ( 120 × 123) / 3
LCM(120,123) = 14760 / 3
LCM(120,123) = 4920

Properties of LCM 120 and 123

(i) The LCM of 123 and 120 is associative

LCM of 120 and 123 = LCM of 123 and 120

Frequently Asked Questions on LCM of 120 and 123

1. What is the LCM of 120 and 123?

Answer: LCM of 120 and 123 is 4920.

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 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.

4. How to Find the LCM of 120 and 123?

Answer:

Least Common Multiple of 120 and 123 = 4920

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 123

123 = 3 x 41

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

LCM = 4920 = 2 x 2 x 2 x 3 x 5 x 41

Step 4: Therefore, the least common multiple of 120 and 123 is 4920.