Least Common Multiple (LCM) of 105 and 194
The least common multiple (LCM) of 105 and 194 is 20370.
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 105 and 194?
First, calculate the GCD of 105 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 194 = 0 remainder 105 |
| 2 | 194 ÷ 105 = 1 remainder 89 |
| 3 | 105 ÷ 89 = 1 remainder 16 |
| 4 | 89 ÷ 16 = 5 remainder 9 |
| 5 | 16 ÷ 9 = 1 remainder 7 |
| 6 | 9 ÷ 7 = 1 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 198 | 6336 |
| 132 and 154 | 924 |
| 61 and 107 | 6527 |
| 162 and 17 | 2754 |
| 180 and 41 | 7380 |