Least Common Multiple (LCM) of 103 and 194
The least common multiple (LCM) of 103 and 194 is 19982.
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 194?
First, calculate the GCD of 103 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 194 = 0 remainder 103 |
| 2 | 194 ÷ 103 = 1 remainder 91 |
| 3 | 103 ÷ 91 = 1 remainder 12 |
| 4 | 91 ÷ 12 = 7 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 31 | 2759 |
| 21 and 19 | 399 |
| 152 and 28 | 1064 |
| 14 and 76 | 532 |
| 32 and 197 | 6304 |