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 |
|---|---|
| 98 and 31 | 3038 |
| 62 and 60 | 1860 |
| 50 and 61 | 3050 |
| 112 and 171 | 19152 |
| 113 and 180 | 20340 |