Least Common Multiple (LCM) of 144 and 82
The least common multiple (LCM) of 144 and 82 is 5904.
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 82?
First, calculate the GCD of 144 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 82 = 1 remainder 62 |
| 2 | 82 ÷ 62 = 1 remainder 20 |
| 3 | 62 ÷ 20 = 3 remainder 2 |
| 4 | 20 ÷ 2 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 105 | 1155 |
| 122 and 64 | 3904 |
| 34 and 103 | 3502 |
| 87 and 49 | 4263 |
| 163 and 138 | 22494 |