Least Common Multiple (LCM) of 165 and 192
The least common multiple (LCM) of 165 and 192 is 10560.
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 192?
First, calculate the GCD of 165 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 192 = 0 remainder 165 |
| 2 | 192 ÷ 165 = 1 remainder 27 |
| 3 | 165 ÷ 27 = 6 remainder 3 |
| 4 | 27 ÷ 3 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 26 | 598 |
| 77 and 97 | 7469 |
| 185 and 189 | 34965 |
| 165 and 198 | 990 |
| 133 and 112 | 2128 |