Least Common Multiple (LCM) of 194 and 144
The least common multiple (LCM) of 194 and 144 is 13968.
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 144?
First, calculate the GCD of 194 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 144 = 1 remainder 50 |
| 2 | 144 ÷ 50 = 2 remainder 44 |
| 3 | 50 ÷ 44 = 1 remainder 6 |
| 4 | 44 ÷ 6 = 7 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 105 | 3360 |
| 184 and 132 | 6072 |
| 31 and 14 | 434 |
| 75 and 28 | 2100 |
| 93 and 23 | 2139 |