Least Common Multiple (LCM) of 198 and 163
The least common multiple (LCM) of 198 and 163 is 32274.
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 198 and 163?
First, calculate the GCD of 198 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 163 = 1 remainder 35 |
| 2 | 163 ÷ 35 = 4 remainder 23 |
| 3 | 35 ÷ 23 = 1 remainder 12 |
| 4 | 23 ÷ 12 = 1 remainder 11 |
| 5 | 12 ÷ 11 = 1 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 128 | 1152 |
| 142 and 165 | 23430 |
| 52 and 165 | 8580 |
| 12 and 150 | 300 |
| 164 and 124 | 5084 |