Least Common Multiple (LCM) of 108 and 173
The least common multiple (LCM) of 108 and 173 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 108 and 173?
First, calculate the GCD of 108 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 173 = 0 remainder 108 |
| 2 | 173 ÷ 108 = 1 remainder 65 |
| 3 | 108 ÷ 65 = 1 remainder 43 |
| 4 | 65 ÷ 43 = 1 remainder 22 |
| 5 | 43 ÷ 22 = 1 remainder 21 |
| 6 | 22 ÷ 21 = 1 remainder 1 |
| 7 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 21 | 1092 |
| 111 and 130 | 14430 |
| 100 and 156 | 3900 |
| 20 and 12 | 60 |
| 171 and 128 | 21888 |