Least Common Multiple (LCM) of 198 and 161
The least common multiple (LCM) of 198 and 161 is 31878.
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 198 and 161?
First, calculate the GCD of 198 and 161 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 161 = 1 remainder 37 |
| 2 | 161 ÷ 37 = 4 remainder 13 |
| 3 | 37 ÷ 13 = 2 remainder 11 |
| 4 | 13 ÷ 11 = 1 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 60 | 60 |
| 23 and 72 | 1656 |
| 191 and 123 | 23493 |
| 39 and 132 | 1716 |
| 199 and 161 | 32039 |