Least Common Multiple (LCM) of 198 and 106
The least common multiple (LCM) of 198 and 106 is 10494.
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 106?
First, calculate the GCD of 198 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 106 = 1 remainder 92 |
| 2 | 106 ÷ 92 = 1 remainder 14 |
| 3 | 92 ÷ 14 = 6 remainder 8 |
| 4 | 14 ÷ 8 = 1 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 143 | 24024 |
| 86 and 137 | 11782 |
| 44 and 199 | 8756 |
| 122 and 14 | 854 |
| 146 and 58 | 4234 |