Least Common Multiple of 109 and 117

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 109 and 117 the smallest integer that is 12753 that is divisible by both numbers.

Least Common Multiple (LCM) of 109 and 117 is 12753.

LCM(109,117) = 12753

LCM of 109 and 117

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

LCM of:
and

Least Common Multiple of 109 and 117

LCM of 109 and 117 is 12753

Least common multiple can be found by multiplying the highest exponent prime factors of 109 and 117. First we will calculate the prime factors of 109 and 117.

Prime Factorization of 109


109 109
1

Prime factors of 109 are 109. Prime factorization of 109 in exponential form is:

109 = 1091

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

Now multiplying the highest exponent prime factors to calculate the LCM of 109 and 117.

LCM(109,117) = 32×131×1091
LCM(109,117) = 12753

Factors of 109

List of positive integer factors of 109 that divides 109 without a remainder.

1, 109

Factors of 117

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

1, 3, 9, 13, 39, 117

Least Common Multiple of 109 and 117 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 109 and 117, than apply into the LCM equation.

GCF(109,117) = 1
LCM(109,117) = ( 109 × 117) / 1
LCM(109,117) = 12753 / 1
LCM(109,117) = 12753

Properties of LCM 109 and 117

(i) The LCM of 117 and 109 is associative

LCM of 109 and 117 = LCM of 117 and 109

Related Least Common Multiples of 109

Related Least Common Multiples of 117

Frequently Asked Questions on LCM of 109 and 117

1. What is the LCM of 109 and 117?

Answer: LCM of 109 and 117 is 12753.

2. What are the Factors of 109?

Answer: Factors of 109 are 1, 109. There are 2 integers that are factors of 109. The greatest factor of 109 is 109.

3. 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.

4. How to Find the LCM of 109 and 117?

Answer:

Least Common Multiple of 109 and 117 = 12753

Step 1: Find the prime factorization of 109

109 = 109

Step 2: Find the prime factorization of 117

117 = 3 x 3 x 13

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

LCM = 12753 = 3 x 3 x 13 x 109

Step 4: Therefore, the least common multiple of 109 and 117 is 12753.