Least Common Multiple (LCM) of 199 and 165
The least common multiple (LCM) of 199 and 165 is 32835.
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 199 and 165?
First, calculate the GCD of 199 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 165 = 1 remainder 34 |
| 2 | 165 ÷ 34 = 4 remainder 29 |
| 3 | 34 ÷ 29 = 1 remainder 5 |
| 4 | 29 ÷ 5 = 5 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 198 | 198 |
| 84 and 192 | 1344 |
| 168 and 38 | 3192 |
| 89 and 153 | 13617 |
| 107 and 12 | 1284 |