Least Common Multiple (LCM) of 177 and 189
The least common multiple (LCM) of 177 and 189 is 11151.
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 177 and 189?
First, calculate the GCD of 177 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 189 = 0 remainder 177 |
| 2 | 189 ÷ 177 = 1 remainder 12 |
| 3 | 177 ÷ 12 = 14 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 131 | 5109 |
| 156 and 189 | 9828 |
| 145 and 38 | 5510 |
| 80 and 198 | 7920 |
| 28 and 67 | 1876 |