Least Common Multiple (LCM) of 165 and 193
The least common multiple (LCM) of 165 and 193 is 31845.
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 193?
First, calculate the GCD of 165 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 193 = 0 remainder 165 |
| 2 | 193 ÷ 165 = 1 remainder 28 |
| 3 | 165 ÷ 28 = 5 remainder 25 |
| 4 | 28 ÷ 25 = 1 remainder 3 |
| 5 | 25 ÷ 3 = 8 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 69 | 552 |
| 165 and 175 | 5775 |
| 170 and 97 | 16490 |
| 188 and 67 | 12596 |
| 22 and 138 | 1518 |