Least Common Multiple (LCM) of 144 and 193
The least common multiple (LCM) of 144 and 193 is 27792.
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 144 and 193?
First, calculate the GCD of 144 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 193 = 0 remainder 144 |
| 2 | 193 ÷ 144 = 1 remainder 49 |
| 3 | 144 ÷ 49 = 2 remainder 46 |
| 4 | 49 ÷ 46 = 1 remainder 3 |
| 5 | 46 ÷ 3 = 15 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 33 | 1551 |
| 14 and 40 | 280 |
| 167 and 126 | 21042 |
| 73 and 13 | 949 |
| 109 and 61 | 6649 |