Least Common Multiple (LCM) of 165 and 195
The least common multiple (LCM) of 165 and 195 is 2145.
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 195?
First, calculate the GCD of 165 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 195 = 0 remainder 165 |
| 2 | 195 ÷ 165 = 1 remainder 30 |
| 3 | 165 ÷ 30 = 5 remainder 15 |
| 4 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 113 | 18758 |
| 34 and 155 | 5270 |
| 31 and 174 | 5394 |
| 190 and 91 | 17290 |
| 33 and 55 | 165 |