Least Common Multiple (LCM) of 117 and 195
The least common multiple (LCM) of 117 and 195 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 117 and 195?
First, calculate the GCD of 117 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 195 = 0 remainder 117 |
| 2 | 195 ÷ 117 = 1 remainder 78 |
| 3 | 117 ÷ 78 = 1 remainder 39 |
| 4 | 78 ÷ 39 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 29 | 4872 |
| 121 and 14 | 1694 |
| 28 and 150 | 2100 |
| 110 and 197 | 21670 |
| 29 and 116 | 116 |