Least Common Multiple of 117 and 135

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 135 the smallest integer that is 1755 that is divisible by both numbers.

Least Common Multiple (LCM) of 117 and 135 is 1755.

LCM(117,135) = 1755

LCM of 117 and 135

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

LCM of:
and

Least Common Multiple of 117 and 135

LCM of 117 and 135 is 1755

Least common multiple can be found by multiplying the highest exponent prime factors of 117 and 135. First we will calculate the prime factors of 117 and 135.

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 135


3 135
3 45
3 15
5 5
1

Prime factors of 135 are 3,5. Prime factorization of 135 in exponential form is:

135 = 33×51

Now multiplying the highest exponent prime factors to calculate the LCM of 117 and 135.

LCM(117,135) = 33×51×131
LCM(117,135) = 1755

Factors of 117

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

1, 3, 9, 13, 39, 117

Factors of 135

List of positive integer factors of 135 that divides 135 without a remainder.

1, 3, 5, 9, 15, 27, 45, 135

Least Common Multiple of 117 and 135 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 135, than apply into the LCM equation.

GCF(117,135) = 9
LCM(117,135) = ( 117 × 135) / 9
LCM(117,135) = 15795 / 9
LCM(117,135) = 1755

Properties of LCM 117 and 135

(i) The LCM of 135 and 117 is associative

LCM of 117 and 135 = LCM of 135 and 117

Related Least Common Multiples of 117

Related Least Common Multiples of 135

Frequently Asked Questions on LCM of 117 and 135

1. What is the LCM of 117 and 135?

Answer: LCM of 117 and 135 is 1755.

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 135?

Answer: Factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135. There are 8 integers that are factors of 135. The greatest factor of 135 is 135.

4. How to Find the LCM of 117 and 135?

Answer:

Least Common Multiple of 117 and 135 = 1755

Step 1: Find the prime factorization of 117

117 = 3 x 3 x 13

Step 2: Find the prime factorization of 135

135 = 3 x 3 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 = 1755 = 3 x 3 x 3 x 5 x 13

Step 4: Therefore, the least common multiple of 117 and 135 is 1755.