Least Common Multiple (LCM) of 115 and 183
The least common multiple (LCM) of 115 and 183 is 21045.
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 115 and 183?
First, calculate the GCD of 115 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 183 = 0 remainder 115 |
| 2 | 183 ÷ 115 = 1 remainder 68 |
| 3 | 115 ÷ 68 = 1 remainder 47 |
| 4 | 68 ÷ 47 = 1 remainder 21 |
| 5 | 47 ÷ 21 = 2 remainder 5 |
| 6 | 21 ÷ 5 = 4 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 12 | 60 |
| 56 and 107 | 5992 |
| 126 and 132 | 2772 |
| 13 and 137 | 1781 |
| 14 and 169 | 2366 |