Least Common Multiple (LCM) of 14 and 143
The least common multiple (LCM) of 14 and 143 is 2002.
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 14 and 143?
First, calculate the GCD of 14 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 143 = 0 remainder 14 |
| 2 | 143 ÷ 14 = 10 remainder 3 |
| 3 | 14 ÷ 3 = 4 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 77 | 9779 |
| 121 and 89 | 10769 |
| 123 and 45 | 1845 |
| 123 and 33 | 1353 |
| 15 and 78 | 390 |