Least Common Multiple (LCM) of 104 and 171
The least common multiple (LCM) of 104 and 171 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 104 and 171?
First, calculate the GCD of 104 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 171 = 0 remainder 104 |
| 2 | 171 ÷ 104 = 1 remainder 67 |
| 3 | 104 ÷ 67 = 1 remainder 37 |
| 4 | 67 ÷ 37 = 1 remainder 30 |
| 5 | 37 ÷ 30 = 1 remainder 7 |
| 6 | 30 ÷ 7 = 4 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 144 | 16272 |
| 110 and 105 | 2310 |
| 35 and 43 | 1505 |
| 53 and 73 | 3869 |
| 189 and 144 | 3024 |