Least Common Multiple (LCM) of 18 and 173
The least common multiple (LCM) of 18 and 173 is 3114.
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 18 and 173?
First, calculate the GCD of 18 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 18 ÷ 173 = 0 remainder 18 |
| 2 | 173 ÷ 18 = 9 remainder 11 |
| 3 | 18 ÷ 11 = 1 remainder 7 |
| 4 | 11 ÷ 7 = 1 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 178 | 2314 |
| 60 and 169 | 10140 |
| 174 and 141 | 8178 |
| 165 and 70 | 2310 |
| 187 and 88 | 1496 |