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 |
|---|---|
| 117 and 33 | 1287 |
| 148 and 138 | 10212 |
| 120 and 98 | 5880 |
| 63 and 13 | 819 |
| 20 and 142 | 1420 |