Least Common Multiple (LCM) of 163 and 197
The least common multiple (LCM) of 163 and 197 is 32111.
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 163 and 197?
First, calculate the GCD of 163 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 197 = 0 remainder 163 |
| 2 | 197 ÷ 163 = 1 remainder 34 |
| 3 | 163 ÷ 34 = 4 remainder 27 |
| 4 | 34 ÷ 27 = 1 remainder 7 |
| 5 | 27 ÷ 7 = 3 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 72 | 504 |
| 137 and 80 | 10960 |
| 167 and 17 | 2839 |
| 191 and 74 | 14134 |
| 19 and 145 | 2755 |