Least Common Multiple (LCM) of 89 and 173
The least common multiple (LCM) of 89 and 173 is 15397.
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 89 and 173?
First, calculate the GCD of 89 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 173 = 0 remainder 89 |
| 2 | 173 ÷ 89 = 1 remainder 84 |
| 3 | 89 ÷ 84 = 1 remainder 5 |
| 4 | 84 ÷ 5 = 16 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 148 | 1480 |
| 178 and 186 | 16554 |
| 198 and 149 | 29502 |
| 105 and 190 | 3990 |
| 42 and 75 | 1050 |