Least Common Multiple (LCM) of 47 and 104
The least common multiple (LCM) of 47 and 104 is 4888.
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 104?
First, calculate the GCD of 47 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 104 = 0 remainder 47 |
| 2 | 104 ÷ 47 = 2 remainder 10 |
| 3 | 47 ÷ 10 = 4 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 163 | 21516 |
| 14 and 49 | 98 |
| 54 and 72 | 216 |
| 22 and 127 | 2794 |
| 130 and 174 | 11310 |