Least Common Multiple (LCM) of 115 and 144
The least common multiple (LCM) of 115 and 144 is 16560.
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 115 and 144?
First, calculate the GCD of 115 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 144 = 0 remainder 115 |
| 2 | 144 ÷ 115 = 1 remainder 29 |
| 3 | 115 ÷ 29 = 3 remainder 28 |
| 4 | 29 ÷ 28 = 1 remainder 1 |
| 5 | 28 ÷ 1 = 28 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 159 | 3975 |
| 50 and 163 | 8150 |
| 80 and 43 | 3440 |
| 127 and 134 | 17018 |
| 19 and 14 | 266 |