Least Common Multiple (LCM) of 89 and 144
The least common multiple (LCM) of 89 and 144 is 12816.
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 144?
First, calculate the GCD of 89 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 144 = 0 remainder 89 |
| 2 | 144 ÷ 89 = 1 remainder 55 |
| 3 | 89 ÷ 55 = 1 remainder 34 |
| 4 | 55 ÷ 34 = 1 remainder 21 |
| 5 | 34 ÷ 21 = 1 remainder 13 |
| 6 | 21 ÷ 13 = 1 remainder 8 |
| 7 | 13 ÷ 8 = 1 remainder 5 |
| 8 | 8 ÷ 5 = 1 remainder 3 |
| 9 | 5 ÷ 3 = 1 remainder 2 |
| 10 | 3 ÷ 2 = 1 remainder 1 |
| 11 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 65 | 10010 |
| 175 and 133 | 3325 |
| 194 and 114 | 11058 |
| 20 and 88 | 440 |
| 169 and 106 | 17914 |