Least Common Multiple (LCM) of 180 and 54
The least common multiple (LCM) of 180 and 54 is 540.
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 54?
First, calculate the GCD of 180 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 54 = 3 remainder 18 |
| 2 | 54 ÷ 18 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 192 | 1344 |
| 12 and 12 | 12 |
| 174 and 168 | 4872 |
| 52 and 26 | 52 |
| 19 and 21 | 399 |