Least Common Multiple (LCM) of 165 and 194
The least common multiple (LCM) of 165 and 194 is 32010.
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 194?
First, calculate the GCD of 165 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 194 = 0 remainder 165 |
| 2 | 194 ÷ 165 = 1 remainder 29 |
| 3 | 165 ÷ 29 = 5 remainder 20 |
| 4 | 29 ÷ 20 = 1 remainder 9 |
| 5 | 20 ÷ 9 = 2 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 87 | 17313 |
| 132 and 108 | 1188 |
| 172 and 62 | 5332 |
| 133 and 39 | 5187 |
| 17 and 97 | 1649 |