Least Common Multiple (LCM) of 114 and 103
The least common multiple (LCM) of 114 and 103 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 114 and 103?
First, calculate the GCD of 114 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 103 = 1 remainder 11 |
| 2 | 103 ÷ 11 = 9 remainder 4 |
| 3 | 11 ÷ 4 = 2 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 135 | 540 |
| 167 and 125 | 20875 |
| 103 and 133 | 13699 |
| 51 and 191 | 9741 |
| 87 and 46 | 4002 |