Least Common Multiple (LCM) of 194 and 142
The least common multiple (LCM) of 194 and 142 is 13774.
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 142?
First, calculate the GCD of 194 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 142 = 1 remainder 52 |
| 2 | 142 ÷ 52 = 2 remainder 38 |
| 3 | 52 ÷ 38 = 1 remainder 14 |
| 4 | 38 ÷ 14 = 2 remainder 10 |
| 5 | 14 ÷ 10 = 1 remainder 4 |
| 6 | 10 ÷ 4 = 2 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 168 | 10920 |
| 52 and 63 | 3276 |
| 186 and 170 | 15810 |
| 87 and 46 | 4002 |
| 65 and 175 | 2275 |