Least Common Multiple (LCM) of 23 and 81
The least common multiple (LCM) of 23 and 81 is 1863.
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 23 and 81?
First, calculate the GCD of 23 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 81 = 0 remainder 23 |
| 2 | 81 ÷ 23 = 3 remainder 12 |
| 3 | 23 ÷ 12 = 1 remainder 11 |
| 4 | 12 ÷ 11 = 1 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 134 | 16482 |
| 35 and 148 | 5180 |
| 120 and 120 | 120 |
| 156 and 146 | 11388 |
| 11 and 13 | 143 |