Least Common Multiple (LCM) of 17 and 125
The least common multiple (LCM) of 17 and 125 is 2125.
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 125?
First, calculate the GCD of 17 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 125 = 0 remainder 17 |
| 2 | 125 ÷ 17 = 7 remainder 6 |
| 3 | 17 ÷ 6 = 2 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 198 | 13464 |
| 144 and 179 | 25776 |
| 175 and 10 | 350 |
| 84 and 139 | 11676 |
| 67 and 181 | 12127 |