Least Common Multiple (LCM) of 47 and 128
The least common multiple (LCM) of 47 and 128 is 6016.
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 47 and 128?
First, calculate the GCD of 47 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 128 = 0 remainder 47 |
| 2 | 128 ÷ 47 = 2 remainder 34 |
| 3 | 47 ÷ 34 = 1 remainder 13 |
| 4 | 34 ÷ 13 = 2 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 133 | 24073 |
| 87 and 100 | 8700 |
| 32 and 65 | 2080 |
| 180 and 145 | 5220 |
| 101 and 73 | 7373 |