Least Common Multiple of 107 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 107 and 112 the smallest integer that is 11984 that is divisible by both numbers.
Least Common Multiple (LCM) of 107 and 112 is 11984.
LCM(107,112) = 11984
LCM of 107 and 112
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 107 and 112 by Prime method
- Least Common Multiple of 107 and 112 with GCF Formula
LCM of 107 and 112 is 11984
Least common multiple can be found by multiplying the highest exponent prime factors of 107 and 112. First we will calculate the prime factors of 107 and 112.
Prime Factorization of 107
| 107 | 107 |
| 1 |
Prime factors of 107 are 107. Prime factorization of 107 in exponential form is:
107 = 1071
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 107 and 112.
LCM(107,112) = 24×71×1071
LCM(107,112) = 11984
Factors of 107
List of positive integer factors of 107 that divides 107 without a remainder.
1, 107
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 107 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 107 and 112, than apply into the LCM equation.
GCF(107,112) = 1
LCM(107,112) = ( 107 × 112) / 1
LCM(107,112) = 11984 / 1
LCM(107,112) = 11984
Properties of LCM 107 and 112
(i) The LCM of 112 and 107 is associative
LCM of 107 and 112 = LCM of 112 and 107
Related Least Common Multiples of 107
Related Least Common Multiples of 112
Frequently Asked Questions on LCM of 107 and 112
1. What is the LCM of 107 and 112?
Answer: LCM of 107 and 112 is 11984.
2. What are the Factors of 107?
Answer: Factors of 107 are 1, 107. There are 2 integers that are factors of 107. The greatest factor of 107 is 107.
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 107 and 112?
Answer:
Least Common Multiple of 107 and 112 = 11984
Step 1: Find the prime factorization of 107
107 = 107
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 = 11984 = 2 x 2 x 2 x 2 x 7 x 107
Step 4: Therefore, the least common multiple of 107 and 112 is 11984.