Least Common Multiple (LCM) of 81 and 145
The least common multiple (LCM) of 81 and 145 is 11745.
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 145?
First, calculate the GCD of 81 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 145 = 0 remainder 81 |
| 2 | 145 ÷ 81 = 1 remainder 64 |
| 3 | 81 ÷ 64 = 1 remainder 17 |
| 4 | 64 ÷ 17 = 3 remainder 13 |
| 5 | 17 ÷ 13 = 1 remainder 4 |
| 6 | 13 ÷ 4 = 3 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 42 | 42 |
| 15 and 161 | 2415 |
| 155 and 37 | 5735 |
| 140 and 33 | 4620 |
| 18 and 39 | 234 |