Least Common Multiple (LCM) of 50 and 189
The least common multiple (LCM) of 50 and 189 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 50 and 189?
First, calculate the GCD of 50 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 189 = 0 remainder 50 |
| 2 | 189 ÷ 50 = 3 remainder 39 |
| 3 | 50 ÷ 39 = 1 remainder 11 |
| 4 | 39 ÷ 11 = 3 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 66 | 660 |
| 130 and 116 | 7540 |
| 58 and 50 | 1450 |
| 87 and 45 | 1305 |
| 119 and 14 | 238 |