Least Common Multiple (LCM) of 73 and 198
The least common multiple (LCM) of 73 and 198 is 14454.
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 73 and 198?
First, calculate the GCD of 73 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 198 = 0 remainder 73 |
| 2 | 198 ÷ 73 = 2 remainder 52 |
| 3 | 73 ÷ 52 = 1 remainder 21 |
| 4 | 52 ÷ 21 = 2 remainder 10 |
| 5 | 21 ÷ 10 = 2 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 72 | 2520 |
| 68 and 33 | 2244 |
| 195 and 163 | 31785 |
| 184 and 195 | 35880 |
| 108 and 13 | 1404 |