Least Common Multiple (LCM) of 104 and 174
The least common multiple (LCM) of 104 and 174 is 9048.
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 104 and 174?
First, calculate the GCD of 104 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 174 = 0 remainder 104 |
| 2 | 174 ÷ 104 = 1 remainder 70 |
| 3 | 104 ÷ 70 = 1 remainder 34 |
| 4 | 70 ÷ 34 = 2 remainder 2 |
| 5 | 34 ÷ 2 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 105 | 6930 |
| 31 and 28 | 868 |
| 156 and 104 | 312 |
| 173 and 60 | 10380 |
| 10 and 63 | 630 |