Least Common Multiple (LCM) of 81 and 133
The least common multiple (LCM) of 81 and 133 is 10773.
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 133?
First, calculate the GCD of 81 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 133 = 0 remainder 81 |
| 2 | 133 ÷ 81 = 1 remainder 52 |
| 3 | 81 ÷ 52 = 1 remainder 29 |
| 4 | 52 ÷ 29 = 1 remainder 23 |
| 5 | 29 ÷ 23 = 1 remainder 6 |
| 6 | 23 ÷ 6 = 3 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 100 | 11900 |
| 115 and 112 | 12880 |
| 45 and 81 | 405 |
| 91 and 99 | 9009 |
| 129 and 171 | 7353 |