Least Common Multiple (LCM) of 133 and 81
The least common multiple (LCM) of 133 and 81 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 133 and 81?
First, calculate the GCD of 133 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 81 = 1 remainder 52 |
| 2 | 81 ÷ 52 = 1 remainder 29 |
| 3 | 52 ÷ 29 = 1 remainder 23 |
| 4 | 29 ÷ 23 = 1 remainder 6 |
| 5 | 23 ÷ 6 = 3 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 99 | 11187 |
| 126 and 162 | 1134 |
| 108 and 154 | 8316 |
| 135 and 140 | 3780 |
| 153 and 115 | 17595 |