Least Common Multiple (LCM) of 109 and 184
The least common multiple (LCM) of 109 and 184 is 20056.
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 184?
First, calculate the GCD of 109 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 184 = 0 remainder 109 |
| 2 | 184 ÷ 109 = 1 remainder 75 |
| 3 | 109 ÷ 75 = 1 remainder 34 |
| 4 | 75 ÷ 34 = 2 remainder 7 |
| 5 | 34 ÷ 7 = 4 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 191 | 20819 |
| 116 and 195 | 22620 |
| 55 and 131 | 7205 |
| 54 and 25 | 1350 |
| 117 and 123 | 4797 |