Least Common Multiple of 114 and 120

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 114 and 120 the smallest integer that is 2280 that is divisible by both numbers.

Least Common Multiple (LCM) of 114 and 120 is 2280.

LCM(114,120) = 2280

LCM of 114 and 120

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

LCM of:
and

Least Common Multiple of 114 and 120

LCM of 114 and 120 is 2280

Least common multiple can be found by multiplying the highest exponent prime factors of 114 and 120. First we will calculate the prime factors of 114 and 120.

Prime Factorization of 114


2 114
3 57
19 19
1

Prime factors of 114 are 2, 3,19. Prime factorization of 114 in exponential form is:

114 = 21×31×191

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

Now multiplying the highest exponent prime factors to calculate the LCM of 114 and 120.

LCM(114,120) = 23×31×51×191
LCM(114,120) = 2280

Factors of 114

List of positive integer factors of 114 that divides 114 without a remainder.

1, 2, 3, 6, 19, 38, 57, 114

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

Least Common Multiple of 114 and 120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 114 and 120, than apply into the LCM equation.

GCF(114,120) = 6
LCM(114,120) = ( 114 × 120) / 6
LCM(114,120) = 13680 / 6
LCM(114,120) = 2280

Properties of LCM 114 and 120

(i) The LCM of 120 and 114 is associative

LCM of 114 and 120 = LCM of 120 and 114

Related Least Common Multiples of 114

Related Least Common Multiples of 120

Frequently Asked Questions on LCM of 114 and 120

1. What is the LCM of 114 and 120?

Answer: LCM of 114 and 120 is 2280.

2. What are the Factors of 114?

Answer: Factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114. There are 8 integers that are factors of 114. The greatest factor of 114 is 114.

3. 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.

4. How to Find the LCM of 114 and 120?

Answer:

Least Common Multiple of 114 and 120 = 2280

Step 1: Find the prime factorization of 114

114 = 2 x 3 x 19

Step 2: Find the prime factorization of 120

120 = 2 x 2 x 2 x 3 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 = 2280 = 2 x 2 x 2 x 3 x 5 x 19

Step 4: Therefore, the least common multiple of 114 and 120 is 2280.