Least Common Multiple (LCM) of 104 and 165
The least common multiple (LCM) of 104 and 165 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 104 and 165?
First, calculate the GCD of 104 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 165 = 0 remainder 104 |
| 2 | 165 ÷ 104 = 1 remainder 61 |
| 3 | 104 ÷ 61 = 1 remainder 43 |
| 4 | 61 ÷ 43 = 1 remainder 18 |
| 5 | 43 ÷ 18 = 2 remainder 7 |
| 6 | 18 ÷ 7 = 2 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 23 | 3036 |
| 33 and 53 | 1749 |
| 17 and 40 | 680 |
| 167 and 143 | 23881 |
| 140 and 96 | 3360 |