Least Common Multiple (LCM) of 81 and 132
The least common multiple (LCM) of 81 and 132 is 3564.
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 132?
First, calculate the GCD of 81 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 132 = 0 remainder 81 |
| 2 | 132 ÷ 81 = 1 remainder 51 |
| 3 | 81 ÷ 51 = 1 remainder 30 |
| 4 | 51 ÷ 30 = 1 remainder 21 |
| 5 | 30 ÷ 21 = 1 remainder 9 |
| 6 | 21 ÷ 9 = 2 remainder 3 |
| 7 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 10 | 330 |
| 30 and 29 | 870 |
| 184 and 168 | 3864 |
| 88 and 82 | 3608 |
| 184 and 194 | 17848 |