Least Common Multiple (LCM) of 195 and 117
The least common multiple (LCM) of 195 and 117 is 585.
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 117?
First, calculate the GCD of 195 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 117 = 1 remainder 78 |
| 2 | 117 ÷ 78 = 1 remainder 39 |
| 3 | 78 ÷ 39 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 119 | 22610 |
| 165 and 165 | 165 |
| 88 and 191 | 16808 |
| 117 and 99 | 1287 |
| 157 and 71 | 11147 |