Least Common Multiple (LCM) of 81 and 135
The least common multiple (LCM) of 81 and 135 is 405.
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 135?
First, calculate the GCD of 81 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 135 = 0 remainder 81 |
| 2 | 135 ÷ 81 = 1 remainder 54 |
| 3 | 81 ÷ 54 = 1 remainder 27 |
| 4 | 54 ÷ 27 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 141 | 19317 |
| 142 and 79 | 11218 |
| 189 and 37 | 6993 |
| 167 and 74 | 12358 |
| 36 and 99 | 396 |