Least Common Multiple (LCM) of 102 and 81
The least common multiple (LCM) of 102 and 81 is 2754.
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 102 and 81?
First, calculate the GCD of 102 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 81 = 1 remainder 21 |
| 2 | 81 ÷ 21 = 3 remainder 18 |
| 3 | 21 ÷ 18 = 1 remainder 3 |
| 4 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 10 | 50 |
| 176 and 33 | 528 |
| 67 and 61 | 4087 |
| 92 and 66 | 3036 |
| 165 and 192 | 10560 |