Least Common Multiple (LCM) of 135 and 81
The least common multiple (LCM) of 135 and 81 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 135 and 81?
First, calculate the GCD of 135 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 81 = 1 remainder 54 |
| 2 | 81 ÷ 54 = 1 remainder 27 |
| 3 | 54 ÷ 27 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 59 | 5782 |
| 159 and 180 | 9540 |
| 58 and 81 | 4698 |
| 119 and 150 | 17850 |
| 107 and 127 | 13589 |