Least Common Multiple (LCM) of 118 and 198
The least common multiple (LCM) of 118 and 198 is 11682.
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 118 and 198?
First, calculate the GCD of 118 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 198 = 0 remainder 118 |
| 2 | 198 ÷ 118 = 1 remainder 80 |
| 3 | 118 ÷ 80 = 1 remainder 38 |
| 4 | 80 ÷ 38 = 2 remainder 4 |
| 5 | 38 ÷ 4 = 9 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 45 | 3465 |
| 34 and 171 | 5814 |
| 60 and 53 | 3180 |
| 67 and 133 | 8911 |
| 133 and 178 | 23674 |