Least Common Multiple (LCM) of 47 and 65
The least common multiple (LCM) of 47 and 65 is 3055.
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 65?
First, calculate the GCD of 47 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 65 = 0 remainder 47 |
| 2 | 65 ÷ 47 = 1 remainder 18 |
| 3 | 47 ÷ 18 = 2 remainder 11 |
| 4 | 18 ÷ 11 = 1 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 132 | 8580 |
| 190 and 26 | 2470 |
| 148 and 126 | 9324 |
| 43 and 51 | 2193 |
| 141 and 107 | 15087 |