Least Common Multiple (LCM) of 81 and 107
The least common multiple (LCM) of 81 and 107 is 8667.
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 107?
First, calculate the GCD of 81 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 107 = 0 remainder 81 |
| 2 | 107 ÷ 81 = 1 remainder 26 |
| 3 | 81 ÷ 26 = 3 remainder 3 |
| 4 | 26 ÷ 3 = 8 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 103 | 14214 |
| 73 and 22 | 1606 |
| 199 and 31 | 6169 |
| 44 and 139 | 6116 |
| 183 and 135 | 8235 |