Least Common Multiple (LCM) of 189 and 180
The least common multiple (LCM) of 189 and 180 is 3780.
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 180?
First, calculate the GCD of 189 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 180 = 1 remainder 9 |
| 2 | 180 ÷ 9 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 120 | 360 |
| 61 and 121 | 7381 |
| 195 and 68 | 13260 |
| 35 and 93 | 3255 |
| 117 and 78 | 234 |