Least Common Multiple (LCM) of 198 and 123
The least common multiple (LCM) of 198 and 123 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 198 and 123?
First, calculate the GCD of 198 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 123 = 1 remainder 75 |
| 2 | 123 ÷ 75 = 1 remainder 48 |
| 3 | 75 ÷ 48 = 1 remainder 27 |
| 4 | 48 ÷ 27 = 1 remainder 21 |
| 5 | 27 ÷ 21 = 1 remainder 6 |
| 6 | 21 ÷ 6 = 3 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 140 | 5740 |
| 72 and 121 | 8712 |
| 42 and 113 | 4746 |
| 128 and 185 | 23680 |
| 12 and 49 | 588 |