Least Common Multiple (LCM) of 171 and 125
The least common multiple (LCM) of 171 and 125 is 21375.
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 171 and 125?
First, calculate the GCD of 171 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 125 = 1 remainder 46 |
| 2 | 125 ÷ 46 = 2 remainder 33 |
| 3 | 46 ÷ 33 = 1 remainder 13 |
| 4 | 33 ÷ 13 = 2 remainder 7 |
| 5 | 13 ÷ 7 = 1 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 31 | 5456 |
| 31 and 67 | 2077 |
| 57 and 158 | 9006 |
| 45 and 160 | 1440 |
| 82 and 180 | 7380 |