Least Common Multiple (LCM) of 78 and 198
The least common multiple (LCM) of 78 and 198 is 2574.
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 78 and 198?
First, calculate the GCD of 78 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 198 = 0 remainder 78 |
| 2 | 198 ÷ 78 = 2 remainder 42 |
| 3 | 78 ÷ 42 = 1 remainder 36 |
| 4 | 42 ÷ 36 = 1 remainder 6 |
| 5 | 36 ÷ 6 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 199 | 27462 |
| 135 and 165 | 1485 |
| 147 and 132 | 6468 |
| 69 and 98 | 6762 |
| 105 and 131 | 13755 |