Least Common Multiple (LCM) of 165 and 173
The least common multiple (LCM) of 165 and 173 is 28545.
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 173?
First, calculate the GCD of 165 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 173 = 0 remainder 165 |
| 2 | 173 ÷ 165 = 1 remainder 8 |
| 3 | 165 ÷ 8 = 20 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 126 | 1008 |
| 170 and 10 | 170 |
| 11 and 65 | 715 |
| 182 and 42 | 546 |
| 27 and 32 | 864 |