Least Common Multiple (LCM) of 174 and 47
The least common multiple (LCM) of 174 and 47 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 174 and 47?
First, calculate the GCD of 174 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 47 = 3 remainder 33 |
| 2 | 47 ÷ 33 = 1 remainder 14 |
| 3 | 33 ÷ 14 = 2 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 190 | 33630 |
| 11 and 127 | 1397 |
| 49 and 24 | 1176 |
| 110 and 78 | 4290 |
| 200 and 72 | 1800 |