Least Common Multiple (LCM) of 103 and 180
The least common multiple (LCM) of 103 and 180 is 18540.
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 180?
First, calculate the GCD of 103 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 180 = 0 remainder 103 |
| 2 | 180 ÷ 103 = 1 remainder 77 |
| 3 | 103 ÷ 77 = 1 remainder 26 |
| 4 | 77 ÷ 26 = 2 remainder 25 |
| 5 | 26 ÷ 25 = 1 remainder 1 |
| 6 | 25 ÷ 1 = 25 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 179 | 12530 |
| 97 and 23 | 2231 |
| 103 and 134 | 13802 |
| 89 and 13 | 1157 |
| 149 and 75 | 11175 |