Least Common Multiple (LCM) of 189 and 173
The least common multiple (LCM) of 189 and 173 is 32697.
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 189 and 173?
First, calculate the GCD of 189 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 173 = 1 remainder 16 |
| 2 | 173 ÷ 16 = 10 remainder 13 |
| 3 | 16 ÷ 13 = 1 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 19 | 209 |
| 71 and 119 | 8449 |
| 122 and 47 | 5734 |
| 14 and 195 | 2730 |
| 175 and 158 | 27650 |