Least Common Multiple of 109 and 110

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 110 the smallest integer that is 11990 that is divisible by both numbers.

Least Common Multiple (LCM) of 109 and 110 is 11990.

LCM(109,110) = 11990

LCM of 109 and 110

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

LCM of:
and

Least Common Multiple of 109 and 110

LCM of 109 and 110 is 11990

Least common multiple can be found by multiplying the highest exponent prime factors of 109 and 110. First we will calculate the prime factors of 109 and 110.

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 110


2 110
5 55
11 11
1

Prime factors of 110 are 2, 5,11. Prime factorization of 110 in exponential form is:

110 = 21×51×111

Now multiplying the highest exponent prime factors to calculate the LCM of 109 and 110.

LCM(109,110) = 21×51×111×1091
LCM(109,110) = 11990

Factors of 109

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

1, 109

Factors of 110

List of positive integer factors of 110 that divides 110 without a remainder.

1, 2, 5, 10, 11, 22, 55, 110

Least Common Multiple of 109 and 110 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 110, than apply into the LCM equation.

GCF(109,110) = 1
LCM(109,110) = ( 109 × 110) / 1
LCM(109,110) = 11990 / 1
LCM(109,110) = 11990

Properties of LCM 109 and 110

(i) The LCM of 110 and 109 is associative

LCM of 109 and 110 = LCM of 110 and 109

Related Least Common Multiples of 109

Related Least Common Multiples of 110

Frequently Asked Questions on LCM of 109 and 110

1. What is the LCM of 109 and 110?

Answer: LCM of 109 and 110 is 11990.

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 110?

Answer: Factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110. There are 8 integers that are factors of 110. The greatest factor of 110 is 110.

4. How to Find the LCM of 109 and 110?

Answer:

Least Common Multiple of 109 and 110 = 11990

Step 1: Find the prime factorization of 109

109 = 109

Step 2: Find the prime factorization of 110

110 = 2 x 5 x 11

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

LCM = 11990 = 2 x 5 x 11 x 109

Step 4: Therefore, the least common multiple of 109 and 110 is 11990.