Least Common Multiple (LCM) of 105 and 173
The least common multiple (LCM) of 105 and 173 is 18165.
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 105 and 173?
First, calculate the GCD of 105 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 173 = 0 remainder 105 |
| 2 | 173 ÷ 105 = 1 remainder 68 |
| 3 | 105 ÷ 68 = 1 remainder 37 |
| 4 | 68 ÷ 37 = 1 remainder 31 |
| 5 | 37 ÷ 31 = 1 remainder 6 |
| 6 | 31 ÷ 6 = 5 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 133 | 266 |
| 120 and 198 | 3960 |
| 156 and 187 | 29172 |
| 17 and 30 | 510 |
| 163 and 157 | 25591 |