Least Common Multiple (LCM) of 111 and 184
The least common multiple (LCM) of 111 and 184 is 20424.
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 111 and 184?
First, calculate the GCD of 111 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 184 = 0 remainder 111 |
| 2 | 184 ÷ 111 = 1 remainder 73 |
| 3 | 111 ÷ 73 = 1 remainder 38 |
| 4 | 73 ÷ 38 = 1 remainder 35 |
| 5 | 38 ÷ 35 = 1 remainder 3 |
| 6 | 35 ÷ 3 = 11 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 38 | 7182 |
| 191 and 48 | 9168 |
| 146 and 53 | 7738 |
| 185 and 100 | 3700 |
| 97 and 144 | 13968 |