Least Common Multiple (LCM) of 30 and 195
The least common multiple (LCM) of 30 and 195 is 390.
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 30 and 195?
First, calculate the GCD of 30 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 195 = 0 remainder 30 |
| 2 | 195 ÷ 30 = 6 remainder 15 |
| 3 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 96 | 6816 |
| 162 and 48 | 1296 |
| 170 and 117 | 19890 |
| 159 and 144 | 7632 |
| 150 and 195 | 1950 |