Least Common Multiple (LCM) of 107 and 125
The least common multiple (LCM) of 107 and 125 is 13375.
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 107 and 125?
First, calculate the GCD of 107 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 125 = 0 remainder 107 |
| 2 | 125 ÷ 107 = 1 remainder 18 |
| 3 | 107 ÷ 18 = 5 remainder 17 |
| 4 | 18 ÷ 17 = 1 remainder 1 |
| 5 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 69 | 12972 |
| 76 and 76 | 76 |
| 151 and 36 | 5436 |
| 100 and 189 | 18900 |
| 157 and 149 | 23393 |