Least Common Multiple (LCM) of 103 and 111
The least common multiple (LCM) of 103 and 111 is 11433.
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 111?
First, calculate the GCD of 103 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 111 = 0 remainder 103 |
| 2 | 111 ÷ 103 = 1 remainder 8 |
| 3 | 103 ÷ 8 = 12 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 94 | 8460 |
| 87 and 104 | 9048 |
| 22 and 121 | 242 |
| 127 and 99 | 12573 |
| 169 and 115 | 19435 |