Least Common Multiple (LCM) of 115 and 182
The least common multiple (LCM) of 115 and 182 is 20930.
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 182?
First, calculate the GCD of 115 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 182 = 0 remainder 115 |
| 2 | 182 ÷ 115 = 1 remainder 67 |
| 3 | 115 ÷ 67 = 1 remainder 48 |
| 4 | 67 ÷ 48 = 1 remainder 19 |
| 5 | 48 ÷ 19 = 2 remainder 10 |
| 6 | 19 ÷ 10 = 1 remainder 9 |
| 7 | 10 ÷ 9 = 1 remainder 1 |
| 8 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 184 | 3312 |
| 69 and 155 | 10695 |
| 54 and 110 | 2970 |
| 105 and 149 | 15645 |
| 116 and 75 | 8700 |