Least Common Multiple (LCM) of 47 and 179
The least common multiple (LCM) of 47 and 179 is 8413.
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 179?
First, calculate the GCD of 47 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 179 = 0 remainder 47 |
| 2 | 179 ÷ 47 = 3 remainder 38 |
| 3 | 47 ÷ 38 = 1 remainder 9 |
| 4 | 38 ÷ 9 = 4 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 66 | 6402 |
| 37 and 42 | 1554 |
| 120 and 185 | 4440 |
| 91 and 182 | 182 |
| 13 and 144 | 1872 |