Least Common Multiple (LCM) of 165 and 104
The least common multiple (LCM) of 165 and 104 is 17160.
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 165 and 104?
First, calculate the GCD of 165 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 104 = 1 remainder 61 |
| 2 | 104 ÷ 61 = 1 remainder 43 |
| 3 | 61 ÷ 43 = 1 remainder 18 |
| 4 | 43 ÷ 18 = 2 remainder 7 |
| 5 | 18 ÷ 7 = 2 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 173 | 17127 |
| 192 and 114 | 3648 |
| 116 and 186 | 10788 |
| 46 and 38 | 874 |
| 197 and 85 | 16745 |