Least Common Multiple (LCM) of 47 and 64
The least common multiple (LCM) of 47 and 64 is 3008.
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 64?
First, calculate the GCD of 47 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 64 = 0 remainder 47 |
| 2 | 64 ÷ 47 = 1 remainder 17 |
| 3 | 47 ÷ 17 = 2 remainder 13 |
| 4 | 17 ÷ 13 = 1 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 107 | 1712 |
| 178 and 142 | 12638 |
| 70 and 40 | 280 |
| 185 and 14 | 2590 |
| 73 and 119 | 8687 |