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 |
|---|---|
| 179 and 150 | 26850 |
| 190 and 76 | 380 |
| 53 and 99 | 5247 |
| 127 and 66 | 8382 |
| 186 and 31 | 186 |