Least Common Multiple (LCM) of 68 and 198
The least common multiple (LCM) of 68 and 198 is 6732.
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 68 and 198?
First, calculate the GCD of 68 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 198 = 0 remainder 68 |
| 2 | 198 ÷ 68 = 2 remainder 62 |
| 3 | 68 ÷ 62 = 1 remainder 6 |
| 4 | 62 ÷ 6 = 10 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 103 | 10506 |
| 199 and 185 | 36815 |
| 31 and 117 | 3627 |
| 177 and 82 | 14514 |
| 137 and 104 | 14248 |