Least Common Multiple (LCM) of 108 and 195
The least common multiple (LCM) of 108 and 195 is 7020.
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 108 and 195?
First, calculate the GCD of 108 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 195 = 0 remainder 108 |
| 2 | 195 ÷ 108 = 1 remainder 87 |
| 3 | 108 ÷ 87 = 1 remainder 21 |
| 4 | 87 ÷ 21 = 4 remainder 3 |
| 5 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 108 | 11772 |
| 43 and 20 | 860 |
| 45 and 172 | 7740 |
| 17 and 60 | 1020 |
| 154 and 120 | 9240 |