Least Common Multiple (LCM) of 103 and 182
The least common multiple (LCM) of 103 and 182 is 18746.
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 103 and 182?
First, calculate the GCD of 103 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 182 = 0 remainder 103 |
| 2 | 182 ÷ 103 = 1 remainder 79 |
| 3 | 103 ÷ 79 = 1 remainder 24 |
| 4 | 79 ÷ 24 = 3 remainder 7 |
| 5 | 24 ÷ 7 = 3 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 51 | 5916 |
| 35 and 156 | 5460 |
| 83 and 43 | 3569 |
| 55 and 200 | 2200 |
| 90 and 137 | 12330 |