Least Common Multiple (LCM) of 189 and 200
The least common multiple (LCM) of 189 and 200 is 37800.
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 200?
First, calculate the GCD of 189 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 200 = 0 remainder 189 |
| 2 | 200 ÷ 189 = 1 remainder 11 |
| 3 | 189 ÷ 11 = 17 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 185 | 6475 |
| 132 and 67 | 8844 |
| 159 and 141 | 7473 |
| 38 and 51 | 1938 |
| 133 and 57 | 399 |