Least Common Multiple (LCM) of 50 and 195
The least common multiple (LCM) of 50 and 195 is 1950.
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 50 and 195?
First, calculate the GCD of 50 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 195 = 0 remainder 50 |
| 2 | 195 ÷ 50 = 3 remainder 45 |
| 3 | 50 ÷ 45 = 1 remainder 5 |
| 4 | 45 ÷ 5 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 54 | 3456 |
| 39 and 11 | 429 |
| 70 and 103 | 7210 |
| 74 and 194 | 7178 |
| 144 and 40 | 720 |