Least Common Multiple (LCM) of 107 and 116
The least common multiple (LCM) of 107 and 116 is 12412.
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 116?
First, calculate the GCD of 107 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 116 = 0 remainder 107 |
| 2 | 116 ÷ 107 = 1 remainder 9 |
| 3 | 107 ÷ 9 = 11 remainder 8 |
| 4 | 9 ÷ 8 = 1 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 94 | 5640 |
| 95 and 76 | 380 |
| 164 and 185 | 30340 |
| 177 and 79 | 13983 |
| 92 and 146 | 6716 |