Least Common Multiple (LCM) of 14 and 22
The least common multiple (LCM) of 14 and 22 is 154.
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 22?
First, calculate the GCD of 14 and 22 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 22 = 0 remainder 14 |
| 2 | 22 ÷ 14 = 1 remainder 8 |
| 3 | 14 ÷ 8 = 1 remainder 6 |
| 4 | 8 ÷ 6 = 1 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 53 | 5565 |
| 28 and 15 | 420 |
| 49 and 181 | 8869 |
| 86 and 90 | 3870 |
| 187 and 89 | 16643 |