Least Common Multiple (LCM) of 165 and 200
The least common multiple (LCM) of 165 and 200 is 6600.
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 200?
First, calculate the GCD of 165 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 200 = 0 remainder 165 |
| 2 | 200 ÷ 165 = 1 remainder 35 |
| 3 | 165 ÷ 35 = 4 remainder 25 |
| 4 | 35 ÷ 25 = 1 remainder 10 |
| 5 | 25 ÷ 10 = 2 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 125 | 1375 |
| 127 and 60 | 7620 |
| 189 and 111 | 6993 |
| 125 and 175 | 875 |
| 191 and 36 | 6876 |