Least Common Multiple (LCM) of 114 and 143
The least common multiple (LCM) of 114 and 143 is 16302.
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 143?
First, calculate the GCD of 114 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 143 = 0 remainder 114 |
| 2 | 143 ÷ 114 = 1 remainder 29 |
| 3 | 114 ÷ 29 = 3 remainder 27 |
| 4 | 29 ÷ 27 = 1 remainder 2 |
| 5 | 27 ÷ 2 = 13 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 15 | 165 |
| 80 and 189 | 15120 |
| 84 and 159 | 4452 |
| 142 and 53 | 7526 |
| 71 and 113 | 8023 |