Least Common Multiple (LCM) of 104 and 198
The least common multiple (LCM) of 104 and 198 is 10296.
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 104 and 198?
First, calculate the GCD of 104 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 198 = 0 remainder 104 |
| 2 | 198 ÷ 104 = 1 remainder 94 |
| 3 | 104 ÷ 94 = 1 remainder 10 |
| 4 | 94 ÷ 10 = 9 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 62 and 71 | 4402 |
| 158 and 163 | 25754 |
| 199 and 179 | 35621 |
| 145 and 10 | 290 |
| 155 and 161 | 24955 |