Least Common Multiple (LCM) of 50 and 198
The least common multiple (LCM) of 50 and 198 is 4950.
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 198?
First, calculate the GCD of 50 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 198 = 0 remainder 50 |
| 2 | 198 ÷ 50 = 3 remainder 48 |
| 3 | 50 ÷ 48 = 1 remainder 2 |
| 4 | 48 ÷ 2 = 24 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 12 | 300 |
| 64 and 123 | 7872 |
| 106 and 115 | 12190 |
| 167 and 41 | 6847 |
| 128 and 113 | 14464 |