Least Common Multiple (LCM) of 171 and 104
The least common multiple (LCM) of 171 and 104 is 17784.
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 171 and 104?
First, calculate the GCD of 171 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 104 = 1 remainder 67 |
| 2 | 104 ÷ 67 = 1 remainder 37 |
| 3 | 67 ÷ 37 = 1 remainder 30 |
| 4 | 37 ÷ 30 = 1 remainder 7 |
| 5 | 30 ÷ 7 = 4 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 105 | 3570 |
| 131 and 30 | 3930 |
| 110 and 89 | 9790 |
| 46 and 54 | 1242 |
| 180 and 190 | 3420 |