Least Common Multiple (LCM) of 14 and 109
The least common multiple (LCM) of 14 and 109 is 1526.
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 109?
First, calculate the GCD of 14 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 109 = 0 remainder 14 |
| 2 | 109 ÷ 14 = 7 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 |
|---|---|
| 196 and 133 | 3724 |
| 18 and 83 | 1494 |
| 148 and 131 | 19388 |
| 172 and 91 | 15652 |
| 69 and 137 | 9453 |