Least Common Multiple (LCM) of 82 and 121
The least common multiple (LCM) of 82 and 121 is 9922.
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 121?
First, calculate the GCD of 82 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 121 = 0 remainder 82 |
| 2 | 121 ÷ 82 = 1 remainder 39 |
| 3 | 82 ÷ 39 = 2 remainder 4 |
| 4 | 39 ÷ 4 = 9 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 19 | 646 |
| 138 and 97 | 13386 |
| 131 and 68 | 8908 |
| 10 and 76 | 380 |
| 183 and 10 | 1830 |