Least Common Multiple (LCM) of 14 and 96
The least common multiple (LCM) of 14 and 96 is 672.
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 96?
First, calculate the GCD of 14 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 96 = 0 remainder 14 |
| 2 | 96 ÷ 14 = 6 remainder 12 |
| 3 | 14 ÷ 12 = 1 remainder 2 |
| 4 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 130 | 21710 |
| 96 and 180 | 1440 |
| 186 and 180 | 5580 |
| 125 and 71 | 8875 |
| 189 and 200 | 37800 |