Least Common Multiple (LCM) of 99 and 195
The least common multiple (LCM) of 99 and 195 is 6435.
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 99 and 195?
First, calculate the GCD of 99 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 195 = 0 remainder 99 |
| 2 | 195 ÷ 99 = 1 remainder 96 |
| 3 | 99 ÷ 96 = 1 remainder 3 |
| 4 | 96 ÷ 3 = 32 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 26 | 52 |
| 57 and 18 | 342 |
| 106 and 190 | 10070 |
| 195 and 27 | 1755 |
| 189 and 200 | 37800 |