Least Common Multiple (LCM) of 47 and 178
The least common multiple (LCM) of 47 and 178 is 8366.
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 178?
First, calculate the GCD of 47 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 178 = 0 remainder 47 |
| 2 | 178 ÷ 47 = 3 remainder 37 |
| 3 | 47 ÷ 37 = 1 remainder 10 |
| 4 | 37 ÷ 10 = 3 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 18 | 846 |
| 64 and 55 | 3520 |
| 191 and 165 | 31515 |
| 40 and 140 | 280 |
| 13 and 144 | 1872 |