Least Common Multiple (LCM) of 189 and 145
The least common multiple (LCM) of 189 and 145 is 27405.
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 145?
First, calculate the GCD of 189 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 145 = 1 remainder 44 |
| 2 | 145 ÷ 44 = 3 remainder 13 |
| 3 | 44 ÷ 13 = 3 remainder 5 |
| 4 | 13 ÷ 5 = 2 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 200 | 27400 |
| 18 and 171 | 342 |
| 78 and 118 | 4602 |
| 129 and 145 | 18705 |
| 180 and 82 | 7380 |