Least Common Multiple (LCM) of 144 and 197
The least common multiple (LCM) of 144 and 197 is 28368.
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 197?
First, calculate the GCD of 144 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 197 = 0 remainder 144 |
| 2 | 197 ÷ 144 = 1 remainder 53 |
| 3 | 144 ÷ 53 = 2 remainder 38 |
| 4 | 53 ÷ 38 = 1 remainder 15 |
| 5 | 38 ÷ 15 = 2 remainder 8 |
| 6 | 15 ÷ 8 = 1 remainder 7 |
| 7 | 8 ÷ 7 = 1 remainder 1 |
| 8 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 183 | 5307 |
| 185 and 76 | 14060 |
| 40 and 22 | 440 |
| 169 and 109 | 18421 |
| 121 and 80 | 9680 |