Least Common Multiple (LCM) of 82 and 133
The least common multiple (LCM) of 82 and 133 is 10906.
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 133?
First, calculate the GCD of 82 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 133 = 0 remainder 82 |
| 2 | 133 ÷ 82 = 1 remainder 51 |
| 3 | 82 ÷ 51 = 1 remainder 31 |
| 4 | 51 ÷ 31 = 1 remainder 20 |
| 5 | 31 ÷ 20 = 1 remainder 11 |
| 6 | 20 ÷ 11 = 1 remainder 9 |
| 7 | 11 ÷ 9 = 1 remainder 2 |
| 8 | 9 ÷ 2 = 4 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 42 | 630 |
| 157 and 29 | 4553 |
| 130 and 119 | 15470 |
| 193 and 43 | 8299 |
| 157 and 68 | 10676 |