Least Common Multiple (LCM) of 82 and 134
The least common multiple (LCM) of 82 and 134 is 5494.
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 134?
First, calculate the GCD of 82 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 134 = 0 remainder 82 |
| 2 | 134 ÷ 82 = 1 remainder 52 |
| 3 | 82 ÷ 52 = 1 remainder 30 |
| 4 | 52 ÷ 30 = 1 remainder 22 |
| 5 | 30 ÷ 22 = 1 remainder 8 |
| 6 | 22 ÷ 8 = 2 remainder 6 |
| 7 | 8 ÷ 6 = 1 remainder 2 |
| 8 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 40 | 1080 |
| 77 and 135 | 10395 |
| 200 and 55 | 2200 |
| 37 and 114 | 4218 |
| 159 and 108 | 5724 |