Least Common Multiple (LCM) of 89 and 165
The least common multiple (LCM) of 89 and 165 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 89 and 165?
First, calculate the GCD of 89 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 165 = 0 remainder 89 |
| 2 | 165 ÷ 89 = 1 remainder 76 |
| 3 | 89 ÷ 76 = 1 remainder 13 |
| 4 | 76 ÷ 13 = 5 remainder 11 |
| 5 | 13 ÷ 11 = 1 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 144 | 25200 |
| 24 and 98 | 1176 |
| 48 and 83 | 3984 |
| 110 and 184 | 10120 |
| 127 and 164 | 20828 |