Least Common Multiple (LCM) of 184 and 109
The least common multiple (LCM) of 184 and 109 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 184 and 109?
First, calculate the GCD of 184 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 184 ÷ 109 = 1 remainder 75 |
| 2 | 109 ÷ 75 = 1 remainder 34 |
| 3 | 75 ÷ 34 = 2 remainder 7 |
| 4 | 34 ÷ 7 = 4 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 19 | 3420 |
| 120 and 117 | 4680 |
| 148 and 106 | 7844 |
| 41 and 67 | 2747 |
| 95 and 178 | 16910 |