Least Common Multiple of 109 and 112
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 112 the smallest integer that is 12208 that is divisible by both numbers.
Least Common Multiple (LCM) of 109 and 112 is 12208.
LCM(109,112) = 12208
LCM of 109 and 112
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 109 and 112 by Prime method
- Least Common Multiple of 109 and 112 with GCF Formula
LCM of 109 and 112 is 12208
Least common multiple can be found by multiplying the highest exponent prime factors of 109 and 112. First we will calculate the prime factors of 109 and 112.
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 112
| 2 | 112 |
| 2 | 56 |
| 2 | 28 |
| 2 | 14 |
| 7 | 7 |
| 1 |
Prime factors of 112 are 2,7. Prime factorization of 112 in exponential form is:
112 = 24×71
Now multiplying the highest exponent prime factors to calculate the LCM of 109 and 112.
LCM(109,112) = 24×71×1091
LCM(109,112) = 12208
Factors of 109
List of positive integer factors of 109 that divides 109 without a remainder.
1, 109
Factors of 112
List of positive integer factors of 112 that divides 112 without a remainder.
1, 2, 4, 7, 8, 14, 16, 28, 56, 112
Least Common Multiple of 109 and 112 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 112, than apply into the LCM equation.
GCF(109,112) = 1
LCM(109,112) = ( 109 × 112) / 1
LCM(109,112) = 12208 / 1
LCM(109,112) = 12208
Properties of LCM 109 and 112
(i) The LCM of 112 and 109 is associative
LCM of 109 and 112 = LCM of 112 and 109
Related Least Common Multiples of 109
Related Least Common Multiples of 112
Frequently Asked Questions on LCM of 109 and 112
1. What is the LCM of 109 and 112?
Answer: LCM of 109 and 112 is 12208.
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 112?
Answer: Factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112. There are 10 integers that are factors of 112. The greatest factor of 112 is 112.
4. How to Find the LCM of 109 and 112?
Answer:
Least Common Multiple of 109 and 112 = 12208
Step 1: Find the prime factorization of 109
109 = 109
Step 2: Find the prime factorization of 112
112 = 2 x 2 x 2 x 2 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 12208 = 2 x 2 x 2 x 2 x 7 x 109
Step 4: Therefore, the least common multiple of 109 and 112 is 12208.