Least Common Multiple (LCM) of 173 and 108
The least common multiple (LCM) of 173 and 108 is 18684.
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 173 and 108?
First, calculate the GCD of 173 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 173 ÷ 108 = 1 remainder 65 |
| 2 | 108 ÷ 65 = 1 remainder 43 |
| 3 | 65 ÷ 43 = 1 remainder 22 |
| 4 | 43 ÷ 22 = 1 remainder 21 |
| 5 | 22 ÷ 21 = 1 remainder 1 |
| 6 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 172 | 3096 |
| 31 and 28 | 868 |
| 135 and 63 | 945 |
| 120 and 27 | 1080 |
| 17 and 162 | 2754 |