Least Common Multiple (LCM) of 81 and 100
The least common multiple (LCM) of 81 and 100 is 8100.
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 100?
First, calculate the GCD of 81 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 100 = 0 remainder 81 |
| 2 | 100 ÷ 81 = 1 remainder 19 |
| 3 | 81 ÷ 19 = 4 remainder 5 |
| 4 | 19 ÷ 5 = 3 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 194 | 8730 |
| 66 and 137 | 9042 |
| 199 and 54 | 10746 |
| 171 and 75 | 4275 |
| 175 and 37 | 6475 |