Least Common Multiple (LCM) of 171 and 197
The least common multiple (LCM) of 171 and 197 is 33687.
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 171 and 197?
First, calculate the GCD of 171 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 197 = 0 remainder 171 |
| 2 | 197 ÷ 171 = 1 remainder 26 |
| 3 | 171 ÷ 26 = 6 remainder 15 |
| 4 | 26 ÷ 15 = 1 remainder 11 |
| 5 | 15 ÷ 11 = 1 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 121 | 4840 |
| 103 and 103 | 103 |
| 85 and 141 | 11985 |
| 141 and 58 | 8178 |
| 60 and 103 | 6180 |