Least Common Multiple (LCM) of 102 and 125
The least common multiple (LCM) of 102 and 125 is 12750.
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 102 and 125?
First, calculate the GCD of 102 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 125 = 0 remainder 102 |
| 2 | 125 ÷ 102 = 1 remainder 23 |
| 3 | 102 ÷ 23 = 4 remainder 10 |
| 4 | 23 ÷ 10 = 2 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 146 | 9198 |
| 140 and 172 | 6020 |
| 149 and 181 | 26969 |
| 161 and 68 | 10948 |
| 177 and 165 | 9735 |