Least Common Multiple of 117 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 117 and 120 the smallest integer that is 4680 that is divisible by both numbers.

Least Common Multiple (LCM) of 117 and 120 is 4680.

LCM(117,120) = 4680

LCM of 117 and 120

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

LCM of:
and

Least Common Multiple of 117 and 120

LCM of 117 and 120 is 4680

Least common multiple can be found by multiplying the highest exponent prime factors of 117 and 120. First we will calculate the prime factors of 117 and 120.

Prime Factorization of 117


3 117
3 39
13 13
1

Prime factors of 117 are 3,13. Prime factorization of 117 in exponential form is:

117 = 32×131

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 117 and 120.

LCM(117,120) = 23×32×51×131
LCM(117,120) = 4680

Factors of 117

List of positive integer factors of 117 that divides 117 without a remainder.

1, 3, 9, 13, 39, 117

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 117 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 117 and 120, than apply into the LCM equation.

GCF(117,120) = 3
LCM(117,120) = ( 117 × 120) / 3
LCM(117,120) = 14040 / 3
LCM(117,120) = 4680

Properties of LCM 117 and 120

(i) The LCM of 120 and 117 is associative

LCM of 117 and 120 = LCM of 120 and 117

Related Least Common Multiples of 117

Related Least Common Multiples of 120

Frequently Asked Questions on LCM of 117 and 120

1. What is the LCM of 117 and 120?

Answer: LCM of 117 and 120 is 4680.

2. What are the Factors of 117?

Answer: Factors of 117 are 1, 3, 9, 13, 39, 117. There are 6 integers that are factors of 117. The greatest factor of 117 is 117.

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 117 and 120?

Answer:

Least Common Multiple of 117 and 120 = 4680

Step 1: Find the prime factorization of 117

117 = 3 x 3 x 13

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 = 4680 = 2 x 2 x 2 x 3 x 3 x 5 x 13

Step 4: Therefore, the least common multiple of 117 and 120 is 4680.