Least Common Multiple (LCM) of 81 and 144
The least common multiple (LCM) of 81 and 144 is 1296.
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 81 and 144?
First, calculate the GCD of 81 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 144 = 0 remainder 81 |
| 2 | 144 ÷ 81 = 1 remainder 63 |
| 3 | 81 ÷ 63 = 1 remainder 18 |
| 4 | 63 ÷ 18 = 3 remainder 9 |
| 5 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 107 | 10807 |
| 25 and 55 | 275 |
| 44 and 145 | 6380 |
| 96 and 112 | 672 |
| 47 and 141 | 141 |