Least Common Multiple (LCM) of 125 and 81
The least common multiple (LCM) of 125 and 81 is 10125.
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 81?
First, calculate the GCD of 125 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 81 = 1 remainder 44 |
| 2 | 81 ÷ 44 = 1 remainder 37 |
| 3 | 44 ÷ 37 = 1 remainder 7 |
| 4 | 37 ÷ 7 = 5 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 83 | 11952 |
| 56 and 180 | 2520 |
| 86 and 133 | 11438 |
| 186 and 147 | 9114 |
| 30 and 54 | 270 |