Least Common Multiple of 120 and 122

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 122 the smallest integer that is 7320 that is divisible by both numbers.

Least Common Multiple (LCM) of 120 and 122 is 7320.

LCM(120,122) = 7320

LCM of 120 and 122

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

LCM of:
and

Least Common Multiple of 120 and 122

LCM of 120 and 122 is 7320

Least common multiple can be found by multiplying the highest exponent prime factors of 120 and 122. First we will calculate the prime factors of 120 and 122.

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 122


2 122
61 61
1

Prime factors of 122 are 2,61. Prime factorization of 122 in exponential form is:

122 = 21×611

Now multiplying the highest exponent prime factors to calculate the LCM of 120 and 122.

LCM(120,122) = 23×31×51×611
LCM(120,122) = 7320

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 122

List of positive integer factors of 122 that divides 122 without a remainder.

1, 2, 61, 122

Least Common Multiple of 120 and 122 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 122, than apply into the LCM equation.

GCF(120,122) = 2
LCM(120,122) = ( 120 × 122) / 2
LCM(120,122) = 14640 / 2
LCM(120,122) = 7320

Properties of LCM 120 and 122

(i) The LCM of 122 and 120 is associative

LCM of 120 and 122 = LCM of 122 and 120

Related Least Common Multiples of 120

Related Least Common Multiples of 122

Frequently Asked Questions on LCM of 120 and 122

1. What is the LCM of 120 and 122?

Answer: LCM of 120 and 122 is 7320.

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 122?

Answer: Factors of 122 are 1, 2, 61, 122. There are 4 integers that are factors of 122. The greatest factor of 122 is 122.

4. How to Find the LCM of 120 and 122?

Answer:

Least Common Multiple of 120 and 122 = 7320

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 122

122 = 2 x 61

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

LCM = 7320 = 2 x 2 x 2 x 3 x 5 x 61

Step 4: Therefore, the least common multiple of 120 and 122 is 7320.