Least Common Multiple (LCM) of 103 and 114
The least common multiple (LCM) of 103 and 114 is 11742.
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 114?
First, calculate the GCD of 103 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 114 = 0 remainder 103 |
| 2 | 114 ÷ 103 = 1 remainder 11 |
| 3 | 103 ÷ 11 = 9 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 114 | 3648 |
| 186 and 75 | 4650 |
| 153 and 78 | 3978 |
| 103 and 138 | 14214 |
| 179 and 198 | 35442 |