Least Common Multiple (LCM) of 177 and 125
The least common multiple (LCM) of 177 and 125 is 22125.
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 125?
First, calculate the GCD of 177 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 125 = 1 remainder 52 |
| 2 | 125 ÷ 52 = 2 remainder 21 |
| 3 | 52 ÷ 21 = 2 remainder 10 |
| 4 | 21 ÷ 10 = 2 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 44 and 197 | 8668 |
| 36 and 84 | 252 |
| 189 and 128 | 24192 |
| 117 and 89 | 10413 |
| 78 and 84 | 1092 |