Least Common Multiple (LCM) of 189 and 45
The least common multiple (LCM) of 189 and 45 is 945.
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 45?
First, calculate the GCD of 189 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 45 = 4 remainder 9 |
| 2 | 45 ÷ 9 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 80 | 80 |
| 122 and 64 | 3904 |
| 178 and 17 | 3026 |
| 53 and 114 | 6042 |
| 74 and 71 | 5254 |