Least Common Multiple (LCM) of 14 and 193
The least common multiple (LCM) of 14 and 193 is 2702.
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 193?
First, calculate the GCD of 14 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 193 = 0 remainder 14 |
| 2 | 193 ÷ 14 = 13 remainder 11 |
| 3 | 14 ÷ 11 = 1 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 64 | 3008 |
| 113 and 55 | 6215 |
| 12 and 41 | 492 |
| 107 and 81 | 8667 |
| 108 and 163 | 17604 |