Least Common Multiple (LCM) of 114 and 185
The least common multiple (LCM) of 114 and 185 is 21090.
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 185?
First, calculate the GCD of 114 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 185 = 0 remainder 114 |
| 2 | 185 ÷ 114 = 1 remainder 71 |
| 3 | 114 ÷ 71 = 1 remainder 43 |
| 4 | 71 ÷ 43 = 1 remainder 28 |
| 5 | 43 ÷ 28 = 1 remainder 15 |
| 6 | 28 ÷ 15 = 1 remainder 13 |
| 7 | 15 ÷ 13 = 1 remainder 2 |
| 8 | 13 ÷ 2 = 6 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 25 | 3450 |
| 196 and 110 | 10780 |
| 147 and 154 | 3234 |
| 39 and 107 | 4173 |
| 45 and 84 | 1260 |