Least Common Multiple (LCM) of 165 and 89
The least common multiple (LCM) of 165 and 89 is 14685.
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 89?
First, calculate the GCD of 165 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 89 = 1 remainder 76 |
| 2 | 89 ÷ 76 = 1 remainder 13 |
| 3 | 76 ÷ 13 = 5 remainder 11 |
| 4 | 13 ÷ 11 = 1 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 97 | 18624 |
| 143 and 85 | 12155 |
| 190 and 125 | 4750 |
| 148 and 96 | 3552 |
| 112 and 72 | 1008 |