Least Common Multiple (LCM) of 68 and 81
The least common multiple (LCM) of 68 and 81 is 5508.
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 68 and 81?
First, calculate the GCD of 68 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 81 = 0 remainder 68 |
| 2 | 81 ÷ 68 = 1 remainder 13 |
| 3 | 68 ÷ 13 = 5 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 173 | 24566 |
| 35 and 83 | 2905 |
| 45 and 112 | 5040 |
| 72 and 198 | 792 |
| 122 and 40 | 2440 |