Least Common Multiple (LCM) of 107 and 112
The least common multiple (LCM) of 107 and 112 is 11984.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 107 and 112?
First, calculate the GCD of 107 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 112 = 0 remainder 107 |
| 2 | 112 ÷ 107 = 1 remainder 5 |
| 3 | 107 ÷ 5 = 21 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 23 | 3036 |
| 158 and 15 | 2370 |
| 31 and 120 | 3720 |
| 152 and 146 | 11096 |
| 53 and 45 | 2385 |