Least Common Multiple (LCM) of 114 and 81
The least common multiple (LCM) of 114 and 81 is 3078.
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 114 and 81?
First, calculate the GCD of 114 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 81 = 1 remainder 33 |
| 2 | 81 ÷ 33 = 2 remainder 15 |
| 3 | 33 ÷ 15 = 2 remainder 3 |
| 4 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 112 | 8176 |
| 15 and 80 | 240 |
| 198 and 127 | 25146 |
| 126 and 101 | 12726 |
| 152 and 68 | 2584 |