Least Common Multiple (LCM) of 50 and 197
The least common multiple (LCM) of 50 and 197 is 9850.
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 197?
First, calculate the GCD of 50 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 197 = 0 remainder 50 |
| 2 | 197 ÷ 50 = 3 remainder 47 |
| 3 | 50 ÷ 47 = 1 remainder 3 |
| 4 | 47 ÷ 3 = 15 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 96 | 6240 |
| 75 and 36 | 900 |
| 134 and 20 | 1340 |
| 33 and 88 | 264 |
| 149 and 13 | 1937 |