Least Common Multiple (LCM) of 200 and 165
The least common multiple (LCM) of 200 and 165 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 200 and 165?
First, calculate the GCD of 200 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 165 = 1 remainder 35 |
| 2 | 165 ÷ 35 = 4 remainder 25 |
| 3 | 35 ÷ 25 = 1 remainder 10 |
| 4 | 25 ÷ 10 = 2 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 116 | 6148 |
| 78 and 36 | 468 |
| 23 and 171 | 3933 |
| 161 and 44 | 7084 |
| 115 and 84 | 9660 |