Least Common Multiple (LCM) of 165 and 189
The least common multiple (LCM) of 165 and 189 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 165 and 189?
First, calculate the GCD of 165 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 189 = 0 remainder 165 |
| 2 | 189 ÷ 165 = 1 remainder 24 |
| 3 | 165 ÷ 24 = 6 remainder 21 |
| 4 | 24 ÷ 21 = 1 remainder 3 |
| 5 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 110 | 5280 |
| 154 and 13 | 2002 |
| 178 and 64 | 5696 |
| 35 and 31 | 1085 |
| 20 and 33 | 660 |