Least Common Multiple (LCM) of 165 and 199
The least common multiple (LCM) of 165 and 199 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 165 and 199?
First, calculate the GCD of 165 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 199 = 0 remainder 165 |
| 2 | 199 ÷ 165 = 1 remainder 34 |
| 3 | 165 ÷ 34 = 4 remainder 29 |
| 4 | 34 ÷ 29 = 1 remainder 5 |
| 5 | 29 ÷ 5 = 5 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 13 | 585 |
| 54 and 196 | 5292 |
| 145 and 160 | 4640 |
| 56 and 194 | 5432 |
| 141 and 169 | 23829 |