Least Common Multiple (LCM) of 75 and 81
The least common multiple (LCM) of 75 and 81 is 2025.
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 75 and 81?
First, calculate the GCD of 75 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 81 = 0 remainder 75 |
| 2 | 81 ÷ 75 = 1 remainder 6 |
| 3 | 75 ÷ 6 = 12 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 99 | 19800 |
| 83 and 167 | 13861 |
| 129 and 48 | 2064 |
| 162 and 29 | 4698 |
| 174 and 58 | 174 |