Least Common Multiple (LCM) of 109 and 116
The least common multiple (LCM) of 109 and 116 is 12644.
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 109 and 116?
First, calculate the GCD of 109 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 116 = 0 remainder 109 |
| 2 | 116 ÷ 109 = 1 remainder 7 |
| 3 | 109 ÷ 7 = 15 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 116 | 12412 |
| 142 and 65 | 9230 |
| 20 and 129 | 2580 |
| 194 and 38 | 3686 |
| 81 and 147 | 3969 |