Least Common Multiple (LCM) of 195 and 108
The least common multiple (LCM) of 195 and 108 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 195 and 108?
First, calculate the GCD of 195 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 108 = 1 remainder 87 |
| 2 | 108 ÷ 87 = 1 remainder 21 |
| 3 | 87 ÷ 21 = 4 remainder 3 |
| 4 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 21 | 1050 |
| 114 and 195 | 7410 |
| 182 and 80 | 7280 |
| 142 and 36 | 2556 |
| 111 and 50 | 5550 |