Least Common Multiple (LCM) of 81 and 114
The least common multiple (LCM) of 81 and 114 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 81 and 114?
First, calculate the GCD of 81 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 114 = 0 remainder 81 |
| 2 | 114 ÷ 81 = 1 remainder 33 |
| 3 | 81 ÷ 33 = 2 remainder 15 |
| 4 | 33 ÷ 15 = 2 remainder 3 |
| 5 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 171 | 17784 |
| 33 and 39 | 429 |
| 164 and 16 | 656 |
| 117 and 119 | 13923 |
| 165 and 11 | 165 |