Least Common Multiple (LCM) of 144 and 182
The least common multiple (LCM) of 144 and 182 is 13104.
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 182?
First, calculate the GCD of 144 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 182 = 0 remainder 144 |
| 2 | 182 ÷ 144 = 1 remainder 38 |
| 3 | 144 ÷ 38 = 3 remainder 30 |
| 4 | 38 ÷ 30 = 1 remainder 8 |
| 5 | 30 ÷ 8 = 3 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 174 | 3306 |
| 37 and 87 | 3219 |
| 168 and 65 | 10920 |
| 192 and 31 | 5952 |
| 140 and 55 | 1540 |