Least Common Multiple (LCM) of 180 and 165
The least common multiple (LCM) of 180 and 165 is 1980.
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 165?
First, calculate the GCD of 180 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 165 = 1 remainder 15 |
| 2 | 165 ÷ 15 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 36 | 324 |
| 14 and 58 | 406 |
| 120 and 59 | 7080 |
| 15 and 63 | 315 |
| 184 and 71 | 13064 |