Least Common Multiple (LCM) of 18 and 81
The least common multiple (LCM) of 18 and 81 is 162.
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 18 and 81?
First, calculate the GCD of 18 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 18 ÷ 81 = 0 remainder 18 |
| 2 | 81 ÷ 18 = 4 remainder 9 |
| 3 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 135 | 4185 |
| 153 and 35 | 5355 |
| 198 and 162 | 1782 |
| 172 and 139 | 23908 |
| 170 and 13 | 2210 |