Least Common Multiple (LCM) of 125 and 177
The least common multiple (LCM) of 125 and 177 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 125 and 177?
First, calculate the GCD of 125 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 177 = 0 remainder 125 |
| 2 | 177 ÷ 125 = 1 remainder 52 |
| 3 | 125 ÷ 52 = 2 remainder 21 |
| 4 | 52 ÷ 21 = 2 remainder 10 |
| 5 | 21 ÷ 10 = 2 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 126 | 504 |
| 14 and 187 | 2618 |
| 52 and 110 | 2860 |
| 198 and 157 | 31086 |
| 164 and 191 | 31324 |