Least Common Multiple (LCM) of 14 and 115
The least common multiple (LCM) of 14 and 115 is 1610.
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 115?
First, calculate the GCD of 14 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 115 = 0 remainder 14 |
| 2 | 115 ÷ 14 = 8 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 |
|---|---|
| 13 and 27 | 351 |
| 128 and 179 | 22912 |
| 66 and 105 | 2310 |
| 39 and 25 | 975 |
| 16 and 50 | 400 |