Least Common Multiple (LCM) of 103 and 125
The least common multiple (LCM) of 103 and 125 is 12875.
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 103 and 125?
First, calculate the GCD of 103 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 125 = 0 remainder 103 |
| 2 | 125 ÷ 103 = 1 remainder 22 |
| 3 | 103 ÷ 22 = 4 remainder 15 |
| 4 | 22 ÷ 15 = 1 remainder 7 |
| 5 | 15 ÷ 7 = 2 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 129 | 18447 |
| 11 and 119 | 1309 |
| 128 and 10 | 640 |
| 121 and 57 | 6897 |
| 66 and 60 | 660 |