Least Common Multiple (LCM) of 173 and 198
The least common multiple (LCM) of 173 and 198 is 34254.
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 173 and 198?
First, calculate the GCD of 173 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 173 ÷ 198 = 0 remainder 173 |
| 2 | 198 ÷ 173 = 1 remainder 25 |
| 3 | 173 ÷ 25 = 6 remainder 23 |
| 4 | 25 ÷ 23 = 1 remainder 2 |
| 5 | 23 ÷ 2 = 11 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 40 | 840 |
| 15 and 198 | 990 |
| 18 and 198 | 198 |
| 79 and 70 | 5530 |
| 161 and 122 | 19642 |