Least Common Multiple (LCM) of 82 and 117
The least common multiple (LCM) of 82 and 117 is 9594.
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 82 and 117?
First, calculate the GCD of 82 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 117 = 0 remainder 82 |
| 2 | 117 ÷ 82 = 1 remainder 35 |
| 3 | 82 ÷ 35 = 2 remainder 12 |
| 4 | 35 ÷ 12 = 2 remainder 11 |
| 5 | 12 ÷ 11 = 1 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 149 | 15943 |
| 96 and 82 | 3936 |
| 100 and 181 | 18100 |
| 31 and 162 | 5022 |
| 161 and 83 | 13363 |