Least Common Multiple (LCM) of 185 and 103
The least common multiple (LCM) of 185 and 103 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 185 and 103?
First, calculate the GCD of 185 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 103 = 1 remainder 82 |
| 2 | 103 ÷ 82 = 1 remainder 21 |
| 3 | 82 ÷ 21 = 3 remainder 19 |
| 4 | 21 ÷ 19 = 1 remainder 2 |
| 5 | 19 ÷ 2 = 9 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 34 | 34 |
| 35 and 97 | 3395 |
| 67 and 160 | 10720 |
| 100 and 14 | 700 |
| 66 and 114 | 1254 |