Least Common Multiple (LCM) of 81 and 68
The least common multiple (LCM) of 81 and 68 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 81 and 68?
First, calculate the GCD of 81 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 68 = 1 remainder 13 |
| 2 | 68 ÷ 13 = 5 remainder 3 |
| 3 | 13 ÷ 3 = 4 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 133 | 14497 |
| 163 and 138 | 22494 |
| 188 and 178 | 16732 |
| 21 and 141 | 987 |
| 197 and 196 | 38612 |