Least Common Multiple (LCM) of 105 and 184
The least common multiple (LCM) of 105 and 184 is 19320.
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 105 and 184?
First, calculate the GCD of 105 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 184 = 0 remainder 105 |
| 2 | 184 ÷ 105 = 1 remainder 79 |
| 3 | 105 ÷ 79 = 1 remainder 26 |
| 4 | 79 ÷ 26 = 3 remainder 1 |
| 5 | 26 ÷ 1 = 26 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 30 | 60 |
| 115 and 111 | 12765 |
| 162 and 125 | 20250 |
| 79 and 86 | 6794 |
| 75 and 198 | 4950 |