Least Common Multiple (LCM) of 123 and 198
The least common multiple (LCM) of 123 and 198 is 8118.
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 123 and 198?
First, calculate the GCD of 123 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 198 = 0 remainder 123 |
| 2 | 198 ÷ 123 = 1 remainder 75 |
| 3 | 123 ÷ 75 = 1 remainder 48 |
| 4 | 75 ÷ 48 = 1 remainder 27 |
| 5 | 48 ÷ 27 = 1 remainder 21 |
| 6 | 27 ÷ 21 = 1 remainder 6 |
| 7 | 21 ÷ 6 = 3 remainder 3 |
| 8 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 25 | 525 |
| 188 and 125 | 23500 |
| 90 and 81 | 810 |
| 63 and 162 | 1134 |
| 106 and 79 | 8374 |