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 |
|---|---|
| 15 and 91 | 1365 |
| 168 and 151 | 25368 |
| 44 and 91 | 4004 |
| 21 and 41 | 861 |
| 195 and 27 | 1755 |