Least Common Multiple (LCM) of 180 and 195
The least common multiple (LCM) of 180 and 195 is 2340.
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 180 and 195?
First, calculate the GCD of 180 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 195 = 0 remainder 180 |
| 2 | 195 ÷ 180 = 1 remainder 15 |
| 3 | 180 ÷ 15 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 30 | 4470 |
| 78 and 60 | 780 |
| 27 and 71 | 1917 |
| 192 and 185 | 35520 |
| 103 and 110 | 11330 |