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 |
|---|---|
| 111 and 107 | 11877 |
| 117 and 142 | 16614 |
| 110 and 137 | 15070 |
| 190 and 116 | 11020 |
| 168 and 145 | 24360 |