Least Common Multiple (LCM) of 107 and 103
The least common multiple (LCM) of 107 and 103 is 11021.
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 103?
First, calculate the GCD of 107 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 103 = 1 remainder 4 |
| 2 | 103 ÷ 4 = 25 remainder 3 |
| 3 | 4 ÷ 3 = 1 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 36 | 576 |
| 100 and 36 | 900 |
| 167 and 118 | 19706 |
| 57 and 199 | 11343 |
| 161 and 125 | 20125 |