Least Common Multiple (LCM) of 67 and 198
The least common multiple (LCM) of 67 and 198 is 13266.
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 67 and 198?
First, calculate the GCD of 67 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 198 = 0 remainder 67 |
| 2 | 198 ÷ 67 = 2 remainder 64 |
| 3 | 67 ÷ 64 = 1 remainder 3 |
| 4 | 64 ÷ 3 = 21 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 159 | 5724 |
| 180 and 77 | 13860 |
| 26 and 22 | 286 |
| 131 and 23 | 3013 |
| 42 and 84 | 84 |