Least Common Multiple (LCM) of 81 and 125
The least common multiple (LCM) of 81 and 125 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 81 and 125?
First, calculate the GCD of 81 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 125 = 0 remainder 81 |
| 2 | 125 ÷ 81 = 1 remainder 44 |
| 3 | 81 ÷ 44 = 1 remainder 37 |
| 4 | 44 ÷ 37 = 1 remainder 7 |
| 5 | 37 ÷ 7 = 5 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 60 | 1260 |
| 25 and 145 | 725 |
| 167 and 132 | 22044 |
| 104 and 62 | 3224 |
| 196 and 16 | 784 |