Least Common Multiple (LCM) of 81 and 105
The least common multiple (LCM) of 81 and 105 is 2835.
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 105?
First, calculate the GCD of 81 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 105 = 0 remainder 81 |
| 2 | 105 ÷ 81 = 1 remainder 24 |
| 3 | 81 ÷ 24 = 3 remainder 9 |
| 4 | 24 ÷ 9 = 2 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 175 | 24325 |
| 35 and 58 | 2030 |
| 134 and 51 | 6834 |
| 62 and 186 | 186 |
| 31 and 133 | 4123 |