Least Common Multiple (LCM) of 165 and 190
The least common multiple (LCM) of 165 and 190 is 6270.
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 190?
First, calculate the GCD of 165 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 190 = 0 remainder 165 |
| 2 | 190 ÷ 165 = 1 remainder 25 |
| 3 | 165 ÷ 25 = 6 remainder 15 |
| 4 | 25 ÷ 15 = 1 remainder 10 |
| 5 | 15 ÷ 10 = 1 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 32 | 1760 |
| 35 and 60 | 420 |
| 105 and 180 | 1260 |
| 46 and 148 | 3404 |
| 171 and 39 | 2223 |