Least Common Multiple (LCM) of 47 and 174
The least common multiple (LCM) of 47 and 174 is 8178.
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 174?
First, calculate the GCD of 47 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 174 = 0 remainder 47 |
| 2 | 174 ÷ 47 = 3 remainder 33 |
| 3 | 47 ÷ 33 = 1 remainder 14 |
| 4 | 33 ÷ 14 = 2 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 173 | 14186 |
| 26 and 113 | 2938 |
| 70 and 31 | 2170 |
| 32 and 144 | 288 |
| 151 and 106 | 16006 |