Least Common Multiple (LCM) of 185 and 144
The least common multiple (LCM) of 185 and 144 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 185 and 144?
First, calculate the GCD of 185 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 144 = 1 remainder 41 |
| 2 | 144 ÷ 41 = 3 remainder 21 |
| 3 | 41 ÷ 21 = 1 remainder 20 |
| 4 | 21 ÷ 20 = 1 remainder 1 |
| 5 | 20 ÷ 1 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 68 | 3604 |
| 149 and 116 | 17284 |
| 123 and 80 | 9840 |
| 18 and 157 | 2826 |
| 181 and 41 | 7421 |