Least Common Multiple (LCM) of 199 and 144
The least common multiple (LCM) of 199 and 144 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 199 and 144?
First, calculate the GCD of 199 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 144 = 1 remainder 55 |
| 2 | 144 ÷ 55 = 2 remainder 34 |
| 3 | 55 ÷ 34 = 1 remainder 21 |
| 4 | 34 ÷ 21 = 1 remainder 13 |
| 5 | 21 ÷ 13 = 1 remainder 8 |
| 6 | 13 ÷ 8 = 1 remainder 5 |
| 7 | 8 ÷ 5 = 1 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 90 | 4230 |
| 61 and 97 | 5917 |
| 187 and 65 | 12155 |
| 178 and 75 | 13350 |
| 138 and 62 | 4278 |