Least Common Multiple (LCM) of 198 and 104
The least common multiple (LCM) of 198 and 104 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 198 and 104?
First, calculate the GCD of 198 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 104 = 1 remainder 94 |
| 2 | 104 ÷ 94 = 1 remainder 10 |
| 3 | 94 ÷ 10 = 9 remainder 4 |
| 4 | 10 ÷ 4 = 2 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 82 | 8118 |
| 184 and 167 | 30728 |
| 199 and 53 | 10547 |
| 148 and 108 | 3996 |
| 179 and 27 | 4833 |