Least Common Multiple (LCM) of 195 and 82
The least common multiple (LCM) of 195 and 82 is 15990.
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 195 and 82?
First, calculate the GCD of 195 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 82 = 2 remainder 31 |
| 2 | 82 ÷ 31 = 2 remainder 20 |
| 3 | 31 ÷ 20 = 1 remainder 11 |
| 4 | 20 ÷ 11 = 1 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 98 | 8820 |
| 196 and 55 | 10780 |
| 50 and 17 | 850 |
| 95 and 29 | 2755 |
| 197 and 23 | 4531 |