Least Common Multiple (LCM) of 144 and 185
The least common multiple (LCM) of 144 and 185 is 26640.
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 185?
First, calculate the GCD of 144 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 185 = 0 remainder 144 |
| 2 | 185 ÷ 144 = 1 remainder 41 |
| 3 | 144 ÷ 41 = 3 remainder 21 |
| 4 | 41 ÷ 21 = 1 remainder 20 |
| 5 | 21 ÷ 20 = 1 remainder 1 |
| 6 | 20 ÷ 1 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 99 | 10197 |
| 13 and 169 | 169 |
| 57 and 113 | 6441 |
| 19 and 84 | 1596 |
| 59 and 91 | 5369 |