Least Common Multiple (LCM) of 189 and 146
The least common multiple (LCM) of 189 and 146 is 27594.
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 146?
First, calculate the GCD of 189 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 146 = 1 remainder 43 |
| 2 | 146 ÷ 43 = 3 remainder 17 |
| 3 | 43 ÷ 17 = 2 remainder 9 |
| 4 | 17 ÷ 9 = 1 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 36 | 2412 |
| 101 and 21 | 2121 |
| 23 and 159 | 3657 |
| 75 and 177 | 4425 |
| 161 and 93 | 14973 |