Least Common Multiple (LCM) of 114 and 184
The least common multiple (LCM) of 114 and 184 is 10488.
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 114 and 184?
First, calculate the GCD of 114 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 184 = 0 remainder 114 |
| 2 | 184 ÷ 114 = 1 remainder 70 |
| 3 | 114 ÷ 70 = 1 remainder 44 |
| 4 | 70 ÷ 44 = 1 remainder 26 |
| 5 | 44 ÷ 26 = 1 remainder 18 |
| 6 | 26 ÷ 18 = 1 remainder 8 |
| 7 | 18 ÷ 8 = 2 remainder 2 |
| 8 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 172 | 7740 |
| 45 and 107 | 4815 |
| 180 and 21 | 1260 |
| 71 and 134 | 9514 |
| 122 and 71 | 8662 |