Least Common Multiple (LCM) of 104 and 170
The least common multiple (LCM) of 104 and 170 is 8840.
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 170?
First, calculate the GCD of 104 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 170 = 0 remainder 104 |
| 2 | 170 ÷ 104 = 1 remainder 66 |
| 3 | 104 ÷ 66 = 1 remainder 38 |
| 4 | 66 ÷ 38 = 1 remainder 28 |
| 5 | 38 ÷ 28 = 1 remainder 10 |
| 6 | 28 ÷ 10 = 2 remainder 8 |
| 7 | 10 ÷ 8 = 1 remainder 2 |
| 8 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 93 | 744 |
| 143 and 169 | 1859 |
| 93 and 75 | 2325 |
| 94 and 21 | 1974 |
| 165 and 123 | 6765 |