Least Common Multiple (LCM) of 134 and 82
The least common multiple (LCM) of 134 and 82 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 134 and 82?
First, calculate the GCD of 134 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 134 ÷ 82 = 1 remainder 52 |
| 2 | 82 ÷ 52 = 1 remainder 30 |
| 3 | 52 ÷ 30 = 1 remainder 22 |
| 4 | 30 ÷ 22 = 1 remainder 8 |
| 5 | 22 ÷ 8 = 2 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 17 | 221 |
| 12 and 49 | 588 |
| 32 and 130 | 2080 |
| 13 and 194 | 2522 |
| 138 and 124 | 8556 |