Least Common Multiple (LCM) of 47 and 173
The least common multiple (LCM) of 47 and 173 is 8131.
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 173?
First, calculate the GCD of 47 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 173 = 0 remainder 47 |
| 2 | 173 ÷ 47 = 3 remainder 32 |
| 3 | 47 ÷ 32 = 1 remainder 15 |
| 4 | 32 ÷ 15 = 2 remainder 2 |
| 5 | 15 ÷ 2 = 7 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 17 | 2295 |
| 25 and 88 | 2200 |
| 151 and 85 | 12835 |
| 49 and 40 | 1960 |
| 101 and 114 | 11514 |