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 |
|---|---|
| 187 and 114 | 21318 |
| 81 and 132 | 3564 |
| 90 and 103 | 9270 |
| 124 and 46 | 2852 |
| 114 and 80 | 4560 |