Least Common Multiple (LCM) of 65 and 180
The least common multiple (LCM) of 65 and 180 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 65 and 180?
First, calculate the GCD of 65 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 180 = 0 remainder 65 |
| 2 | 180 ÷ 65 = 2 remainder 50 |
| 3 | 65 ÷ 50 = 1 remainder 15 |
| 4 | 50 ÷ 15 = 3 remainder 5 |
| 5 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 14 | 504 |
| 186 and 58 | 5394 |
| 70 and 97 | 6790 |
| 32 and 188 | 1504 |
| 48 and 123 | 1968 |