Least Common Multiple (LCM) of 109 and 86
The least common multiple (LCM) of 109 and 86 is 9374.
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 86?
First, calculate the GCD of 109 and 86 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 86 = 1 remainder 23 |
| 2 | 86 ÷ 23 = 3 remainder 17 |
| 3 | 23 ÷ 17 = 1 remainder 6 |
| 4 | 17 ÷ 6 = 2 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 62 | 5146 |
| 72 and 182 | 6552 |
| 31 and 113 | 3503 |
| 109 and 43 | 4687 |
| 117 and 39 | 117 |