Least Common Multiple (LCM) of 47 and 163
The least common multiple (LCM) of 47 and 163 is 7661.
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 163?
First, calculate the GCD of 47 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 163 = 0 remainder 47 |
| 2 | 163 ÷ 47 = 3 remainder 22 |
| 3 | 47 ÷ 22 = 2 remainder 3 |
| 4 | 22 ÷ 3 = 7 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 54 | 2862 |
| 53 and 178 | 9434 |
| 171 and 116 | 19836 |
| 178 and 38 | 3382 |
| 45 and 116 | 5220 |