Least Common Multiple (LCM) of 107 and 82
The least common multiple (LCM) of 107 and 82 is 8774.
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 82?
First, calculate the GCD of 107 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 82 = 1 remainder 25 |
| 2 | 82 ÷ 25 = 3 remainder 7 |
| 3 | 25 ÷ 7 = 3 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 154 | 16786 |
| 152 and 116 | 4408 |
| 31 and 125 | 3875 |
| 184 and 192 | 4416 |
| 171 and 51 | 2907 |