Least Common Multiple (LCM) of 17 and 177
The least common multiple (LCM) of 17 and 177 is 3009.
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 17 and 177?
First, calculate the GCD of 17 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 177 = 0 remainder 17 |
| 2 | 177 ÷ 17 = 10 remainder 7 |
| 3 | 17 ÷ 7 = 2 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 123 | 7872 |
| 52 and 170 | 4420 |
| 111 and 40 | 4440 |
| 83 and 119 | 9877 |
| 169 and 122 | 20618 |