Least Common Multiple (LCM) of 194 and 75
The least common multiple (LCM) of 194 and 75 is 14550.
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 194 and 75?
First, calculate the GCD of 194 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 75 = 2 remainder 44 |
| 2 | 75 ÷ 44 = 1 remainder 31 |
| 3 | 44 ÷ 31 = 1 remainder 13 |
| 4 | 31 ÷ 13 = 2 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 21 | 357 |
| 142 and 178 | 12638 |
| 111 and 116 | 12876 |
| 72 and 63 | 504 |
| 126 and 135 | 1890 |