Least Common Multiple of 109 and 116
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 116 the smallest integer that is 12644 that is divisible by both numbers.
Least Common Multiple (LCM) of 109 and 116 is 12644.
LCM(109,116) = 12644
LCM of 109 and 116
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 109 and 116 by Prime method
- Least Common Multiple of 109 and 116 with GCF Formula
LCM of 109 and 116 is 12644
Least common multiple can be found by multiplying the highest exponent prime factors of 109 and 116. First we will calculate the prime factors of 109 and 116.
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 116
| 2 | 116 |
| 2 | 58 |
| 29 | 29 |
| 1 |
Prime factors of 116 are 2,29. Prime factorization of 116 in exponential form is:
116 = 22×291
Now multiplying the highest exponent prime factors to calculate the LCM of 109 and 116.
LCM(109,116) = 22×291×1091
LCM(109,116) = 12644
Factors of 109
List of positive integer factors of 109 that divides 109 without a remainder.
1, 109
Factors of 116
List of positive integer factors of 116 that divides 116 without a remainder.
1, 2, 4, 29, 58, 116
Least Common Multiple of 109 and 116 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 116, than apply into the LCM equation.
GCF(109,116) = 1
LCM(109,116) = ( 109 × 116) / 1
LCM(109,116) = 12644 / 1
LCM(109,116) = 12644
Properties of LCM 109 and 116
(i) The LCM of 116 and 109 is associative
LCM of 109 and 116 = LCM of 116 and 109
Related Least Common Multiples of 109
Related Least Common Multiples of 116
Frequently Asked Questions on LCM of 109 and 116
1. What is the LCM of 109 and 116?
Answer: LCM of 109 and 116 is 12644.
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 116?
Answer: Factors of 116 are 1, 2, 4, 29, 58, 116. There are 6 integers that are factors of 116. The greatest factor of 116 is 116.
4. How to Find the LCM of 109 and 116?
Answer:
Least Common Multiple of 109 and 116 = 12644
Step 1: Find the prime factorization of 109
109 = 109
Step 2: Find the prime factorization of 116
116 = 2 x 2 x 29
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 12644 = 2 x 2 x 29 x 109
Step 4: Therefore, the least common multiple of 109 and 116 is 12644.
