Least Common Multiple (LCM) of 189 and 194
The least common multiple (LCM) of 189 and 194 is 36666.
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 194?
First, calculate the GCD of 189 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 194 = 0 remainder 189 |
| 2 | 194 ÷ 189 = 1 remainder 5 |
| 3 | 189 ÷ 5 = 37 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 15 | 600 |
| 42 and 135 | 1890 |
| 146 and 151 | 22046 |
| 13 and 89 | 1157 |
| 17 and 88 | 1496 |