Least Common Multiple of 120 and 126

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 126 the smallest integer that is 2520 that is divisible by both numbers.

Least Common Multiple (LCM) of 120 and 126 is 2520.

LCM(120,126) = 2520

LCM of 120 and 126

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

LCM of:
and

Least Common Multiple of 120 and 126

LCM of 120 and 126 is 2520

Least common multiple can be found by multiplying the highest exponent prime factors of 120 and 126. First we will calculate the prime factors of 120 and 126.

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 126


2 126
3 63
3 21
7 7
1

Prime factors of 126 are 2, 3,7. Prime factorization of 126 in exponential form is:

126 = 21×32×71

Now multiplying the highest exponent prime factors to calculate the LCM of 120 and 126.

LCM(120,126) = 23×32×51×71
LCM(120,126) = 2520

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 126

List of positive integer factors of 126 that divides 126 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126

Least Common Multiple of 120 and 126 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 126, than apply into the LCM equation.

GCF(120,126) = 6
LCM(120,126) = ( 120 × 126) / 6
LCM(120,126) = 15120 / 6
LCM(120,126) = 2520

Properties of LCM 120 and 126

(i) The LCM of 126 and 120 is associative

LCM of 120 and 126 = LCM of 126 and 120

Related Least Common Multiples of 120

Related Least Common Multiples of 126

Frequently Asked Questions on LCM of 120 and 126

1. What is the LCM of 120 and 126?

Answer: LCM of 120 and 126 is 2520.

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 126?

Answer: Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126. There are 12 integers that are factors of 126. The greatest factor of 126 is 126.

4. How to Find the LCM of 120 and 126?

Answer:

Least Common Multiple of 120 and 126 = 2520

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 126

126 = 2 x 3 x 3 x 7

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

LCM = 2520 = 2 x 2 x 2 x 3 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 120 and 126 is 2520.