Least Common Multiple (LCM) of 117 and 198
The least common multiple (LCM) of 117 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 117 and 198?
First, calculate the GCD of 117 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 198 = 0 remainder 117 |
| 2 | 198 ÷ 117 = 1 remainder 81 |
| 3 | 117 ÷ 81 = 1 remainder 36 |
| 4 | 81 ÷ 36 = 2 remainder 9 |
| 5 | 36 ÷ 9 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 15 | 720 |
| 101 and 154 | 15554 |
| 51 and 142 | 7242 |
| 46 and 107 | 4922 |
| 24 and 42 | 168 |