Least Common Multiple (LCM) of 117 and 82
The least common multiple (LCM) of 117 and 82 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 117 and 82?
First, calculate the GCD of 117 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 82 = 1 remainder 35 |
| 2 | 82 ÷ 35 = 2 remainder 12 |
| 3 | 35 ÷ 12 = 2 remainder 11 |
| 4 | 12 ÷ 11 = 1 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 102 | 1122 |
| 162 and 190 | 15390 |
| 149 and 105 | 15645 |
| 197 and 23 | 4531 |
| 63 and 41 | 2583 |