Least Common Multiple (LCM) of 103 and 185
The least common multiple (LCM) of 103 and 185 is 19055.
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 185?
First, calculate the GCD of 103 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 185 = 0 remainder 103 |
| 2 | 185 ÷ 103 = 1 remainder 82 |
| 3 | 103 ÷ 82 = 1 remainder 21 |
| 4 | 82 ÷ 21 = 3 remainder 19 |
| 5 | 21 ÷ 19 = 1 remainder 2 |
| 6 | 19 ÷ 2 = 9 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 73 | 8979 |
| 15 and 36 | 180 |
| 148 and 107 | 15836 |
| 60 and 14 | 420 |
| 165 and 47 | 7755 |