Least Common Multiple (LCM) of 165 and 197
The least common multiple (LCM) of 165 and 197 is 32505.
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 165 and 197?
First, calculate the GCD of 165 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 197 = 0 remainder 165 |
| 2 | 197 ÷ 165 = 1 remainder 32 |
| 3 | 165 ÷ 32 = 5 remainder 5 |
| 4 | 32 ÷ 5 = 6 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 89 | 13439 |
| 177 and 191 | 33807 |
| 41 and 128 | 5248 |
| 50 and 81 | 4050 |
| 20 and 68 | 340 |