Least Common Multiple (LCM) of 47 and 198
The least common multiple (LCM) of 47 and 198 is 9306.
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 47 and 198?
First, calculate the GCD of 47 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 198 = 0 remainder 47 |
| 2 | 198 ÷ 47 = 4 remainder 10 |
| 3 | 47 ÷ 10 = 4 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 138 | 10212 |
| 144 and 192 | 576 |
| 86 and 114 | 4902 |
| 37 and 34 | 1258 |
| 109 and 172 | 18748 |