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 |
|---|---|
| 114 and 180 | 3420 |
| 142 and 178 | 12638 |
| 174 and 39 | 2262 |
| 169 and 31 | 5239 |
| 111 and 50 | 5550 |