Least Common Multiple (LCM) of 194 and 82
The least common multiple (LCM) of 194 and 82 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 194 and 82?
First, calculate the GCD of 194 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 82 = 2 remainder 30 |
| 2 | 82 ÷ 30 = 2 remainder 22 |
| 3 | 30 ÷ 22 = 1 remainder 8 |
| 4 | 22 ÷ 8 = 2 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 145 | 11890 |
| 187 and 65 | 12155 |
| 59 and 97 | 5723 |
| 80 and 115 | 1840 |
| 102 and 190 | 9690 |