Least Common Multiple (LCM) of 81 and 128
The least common multiple (LCM) of 81 and 128 is 10368.
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 128?
First, calculate the GCD of 81 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 128 = 0 remainder 81 |
| 2 | 128 ÷ 81 = 1 remainder 47 |
| 3 | 81 ÷ 47 = 1 remainder 34 |
| 4 | 47 ÷ 34 = 1 remainder 13 |
| 5 | 34 ÷ 13 = 2 remainder 8 |
| 6 | 13 ÷ 8 = 1 remainder 5 |
| 7 | 8 ÷ 5 = 1 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 31 | 5239 |
| 10 and 136 | 680 |
| 149 and 15 | 2235 |
| 106 and 69 | 7314 |
| 67 and 61 | 4087 |