Least Common Multiple (LCM) of 195 and 17
The least common multiple (LCM) of 195 and 17 is 3315.
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 17?
First, calculate the GCD of 195 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 17 = 11 remainder 8 |
| 2 | 17 ÷ 8 = 2 remainder 1 |
| 3 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 123 | 6765 |
| 82 and 189 | 15498 |
| 117 and 38 | 4446 |
| 104 and 92 | 2392 |
| 21 and 60 | 420 |