Least Common Multiple (LCM) of 189 and 50
The least common multiple (LCM) of 189 and 50 is 9450.
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 189 and 50?
First, calculate the GCD of 189 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 50 = 3 remainder 39 |
| 2 | 50 ÷ 39 = 1 remainder 11 |
| 3 | 39 ÷ 11 = 3 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 98 | 980 |
| 187 and 112 | 20944 |
| 48 and 62 | 1488 |
| 168 and 54 | 1512 |
| 189 and 195 | 12285 |