Least Common Multiple (LCM) of 14 and 24
The least common multiple (LCM) of 14 and 24 is 168.
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 24?
First, calculate the GCD of 14 and 24 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 24 = 0 remainder 14 |
| 2 | 24 ÷ 14 = 1 remainder 10 |
| 3 | 14 ÷ 10 = 1 remainder 4 |
| 4 | 10 ÷ 4 = 2 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 145 | 18705 |
| 56 and 47 | 2632 |
| 149 and 41 | 6109 |
| 97 and 57 | 5529 |
| 192 and 59 | 11328 |