Least Common Multiple (LCM) of 67 and 81
The least common multiple (LCM) of 67 and 81 is 5427.
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 67 and 81?
First, calculate the GCD of 67 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 81 = 0 remainder 67 |
| 2 | 81 ÷ 67 = 1 remainder 14 |
| 3 | 67 ÷ 14 = 4 remainder 11 |
| 4 | 14 ÷ 11 = 1 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 191 | 2674 |
| 95 and 49 | 4655 |
| 81 and 113 | 9153 |
| 21 and 77 | 231 |
| 134 and 179 | 23986 |