Least Common Multiple (LCM) of 198 and 68
The least common multiple (LCM) of 198 and 68 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 198 and 68?
First, calculate the GCD of 198 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 68 = 2 remainder 62 |
| 2 | 68 ÷ 62 = 1 remainder 6 |
| 3 | 62 ÷ 6 = 10 remainder 2 |
| 4 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 136 | 408 |
| 36 and 126 | 252 |
| 175 and 187 | 32725 |
| 25 and 152 | 3800 |
| 200 and 166 | 16600 |