Least Common Multiple (LCM) of 81 and 30
The least common multiple (LCM) of 81 and 30 is 810.
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 30?
First, calculate the GCD of 81 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 30 = 2 remainder 21 |
| 2 | 30 ÷ 21 = 1 remainder 9 |
| 3 | 21 ÷ 9 = 2 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 110 | 660 |
| 149 and 74 | 11026 |
| 156 and 61 | 9516 |
| 185 and 80 | 2960 |
| 200 and 178 | 17800 |