Least Common Multiple (LCM) of 173 and 178
The least common multiple (LCM) of 173 and 178 is 30794.
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 178?
First, calculate the GCD of 173 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 173 ÷ 178 = 0 remainder 173 |
| 2 | 178 ÷ 173 = 1 remainder 5 |
| 3 | 173 ÷ 5 = 34 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 104 | 17784 |
| 49 and 181 | 8869 |
| 177 and 180 | 10620 |
| 77 and 190 | 14630 |
| 116 and 22 | 1276 |