Least Common Multiple (LCM) of 82 and 194
The least common multiple (LCM) of 82 and 194 is 7954.
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 194?
First, calculate the GCD of 82 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 194 = 0 remainder 82 |
| 2 | 194 ÷ 82 = 2 remainder 30 |
| 3 | 82 ÷ 30 = 2 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 |
|---|---|
| 56 and 15 | 840 |
| 189 and 191 | 36099 |
| 130 and 173 | 22490 |
| 112 and 28 | 112 |
| 129 and 185 | 23865 |