Least Common Multiple (LCM) of 125 and 109
The least common multiple (LCM) of 125 and 109 is 13625.
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 109?
First, calculate the GCD of 125 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 109 = 1 remainder 16 |
| 2 | 109 ÷ 16 = 6 remainder 13 |
| 3 | 16 ÷ 13 = 1 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 53 | 1961 |
| 199 and 127 | 25273 |
| 90 and 160 | 1440 |
| 63 and 114 | 2394 |
| 16 and 82 | 656 |