Least Common Multiple (LCM) of 161 and 197
The least common multiple (LCM) of 161 and 197 is 31717.
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 161 and 197?
First, calculate the GCD of 161 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 161 ÷ 197 = 0 remainder 161 |
| 2 | 197 ÷ 161 = 1 remainder 36 |
| 3 | 161 ÷ 36 = 4 remainder 17 |
| 4 | 36 ÷ 17 = 2 remainder 2 |
| 5 | 17 ÷ 2 = 8 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 68 | 1700 |
| 14 and 100 | 700 |
| 145 and 119 | 17255 |
| 84 and 181 | 15204 |
| 165 and 94 | 15510 |