Least Common Multiple of 120 and 125

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 125 the smallest integer that is 3000 that is divisible by both numbers.

Least Common Multiple (LCM) of 120 and 125 is 3000.

LCM(120,125) = 3000

LCM of 120 and 125

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

LCM of:
and

Least Common Multiple of 120 and 125

LCM of 120 and 125 is 3000

Least common multiple can be found by multiplying the highest exponent prime factors of 120 and 125. First we will calculate the prime factors of 120 and 125.

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 125


5 125
5 25
5 5
1

Prime factors of 125 are 5. Prime factorization of 125 in exponential form is:

125 = 53

Now multiplying the highest exponent prime factors to calculate the LCM of 120 and 125.

LCM(120,125) = 23×31×53
LCM(120,125) = 3000

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 125

List of positive integer factors of 125 that divides 125 without a remainder.

1, 5, 25, 125

Least Common Multiple of 120 and 125 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 125, than apply into the LCM equation.

GCF(120,125) = 5
LCM(120,125) = ( 120 × 125) / 5
LCM(120,125) = 15000 / 5
LCM(120,125) = 3000

Properties of LCM 120 and 125

(i) The LCM of 125 and 120 is associative

LCM of 120 and 125 = LCM of 125 and 120

Related Least Common Multiples of 120

Related Least Common Multiples of 125

Frequently Asked Questions on LCM of 120 and 125

1. What is the LCM of 120 and 125?

Answer: LCM of 120 and 125 is 3000.

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 125?

Answer: Factors of 125 are 1, 5, 25, 125. There are 4 integers that are factors of 125. The greatest factor of 125 is 125.

4. How to Find the LCM of 120 and 125?

Answer:

Least Common Multiple of 120 and 125 = 3000

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 125

125 = 5 x 5 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 = 3000 = 2 x 2 x 2 x 3 x 5 x 5 x 5

Step 4: Therefore, the least common multiple of 120 and 125 is 3000.