Least Common Multiple (LCM) of 189 and 165
The least common multiple (LCM) of 189 and 165 is 10395.
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 189 and 165?
First, calculate the GCD of 189 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 165 = 1 remainder 24 |
| 2 | 165 ÷ 24 = 6 remainder 21 |
| 3 | 24 ÷ 21 = 1 remainder 3 |
| 4 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 196 | 24500 |
| 44 and 60 | 660 |
| 170 and 24 | 2040 |
| 97 and 84 | 8148 |
| 91 and 178 | 16198 |