Least Common Multiple (LCM) of 103 and 109
The least common multiple (LCM) of 103 and 109 is 11227.
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 109?
First, calculate the GCD of 103 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 109 = 0 remainder 103 |
| 2 | 109 ÷ 103 = 1 remainder 6 |
| 3 | 103 ÷ 6 = 17 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 60 | 3180 |
| 112 and 120 | 1680 |
| 109 and 101 | 11009 |
| 178 and 144 | 12816 |
| 122 and 144 | 8784 |