Least Common Multiple (LCM) of 144 and 199
The least common multiple (LCM) of 144 and 199 is 28656.
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 199?
First, calculate the GCD of 144 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 199 = 0 remainder 144 |
| 2 | 199 ÷ 144 = 1 remainder 55 |
| 3 | 144 ÷ 55 = 2 remainder 34 |
| 4 | 55 ÷ 34 = 1 remainder 21 |
| 5 | 34 ÷ 21 = 1 remainder 13 |
| 6 | 21 ÷ 13 = 1 remainder 8 |
| 7 | 13 ÷ 8 = 1 remainder 5 |
| 8 | 8 ÷ 5 = 1 remainder 3 |
| 9 | 5 ÷ 3 = 1 remainder 2 |
| 10 | 3 ÷ 2 = 1 remainder 1 |
| 11 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 97 | 18624 |
| 56 and 126 | 504 |
| 83 and 82 | 6806 |
| 140 and 51 | 7140 |
| 166 and 163 | 27058 |