Least Common Multiple (LCM) of 82 and 137
The least common multiple (LCM) of 82 and 137 is 11234.
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 137?
First, calculate the GCD of 82 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 137 = 0 remainder 82 |
| 2 | 137 ÷ 82 = 1 remainder 55 |
| 3 | 82 ÷ 55 = 1 remainder 27 |
| 4 | 55 ÷ 27 = 2 remainder 1 |
| 5 | 27 ÷ 1 = 27 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 50 | 1450 |
| 62 and 12 | 372 |
| 81 and 11 | 891 |
| 147 and 65 | 9555 |
| 93 and 80 | 7440 |