Least Common Multiple (LCM) of 165 and 184
The least common multiple (LCM) of 165 and 184 is 30360.
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 184?
First, calculate the GCD of 165 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 184 = 0 remainder 165 |
| 2 | 184 ÷ 165 = 1 remainder 19 |
| 3 | 165 ÷ 19 = 8 remainder 13 |
| 4 | 19 ÷ 13 = 1 remainder 6 |
| 5 | 13 ÷ 6 = 2 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 128 | 13440 |
| 123 and 196 | 24108 |
| 92 and 145 | 13340 |
| 125 and 192 | 24000 |
| 10 and 49 | 490 |