Least Common Multiple (LCM) of 114 and 125
The least common multiple (LCM) of 114 and 125 is 14250.
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 114 and 125?
First, calculate the GCD of 114 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 125 = 0 remainder 114 |
| 2 | 125 ÷ 114 = 1 remainder 11 |
| 3 | 114 ÷ 11 = 10 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 50 | 4850 |
| 65 and 13 | 65 |
| 87 and 82 | 7134 |
| 128 and 61 | 7808 |
| 92 and 183 | 16836 |