Least Common Multiple (LCM) of 54 and 198
The least common multiple (LCM) of 54 and 198 is 594.
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 54 and 198?
First, calculate the GCD of 54 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 198 = 0 remainder 54 |
| 2 | 198 ÷ 54 = 3 remainder 36 |
| 3 | 54 ÷ 36 = 1 remainder 18 |
| 4 | 36 ÷ 18 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 87 | 9570 |
| 179 and 104 | 18616 |
| 180 and 26 | 2340 |
| 91 and 25 | 2275 |
| 178 and 164 | 14596 |