Least Common Multiple (LCM) of 144 and 89
The least common multiple (LCM) of 144 and 89 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 144 and 89?
First, calculate the GCD of 144 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 89 = 1 remainder 55 |
| 2 | 89 ÷ 55 = 1 remainder 34 |
| 3 | 55 ÷ 34 = 1 remainder 21 |
| 4 | 34 ÷ 21 = 1 remainder 13 |
| 5 | 21 ÷ 13 = 1 remainder 8 |
| 6 | 13 ÷ 8 = 1 remainder 5 |
| 7 | 8 ÷ 5 = 1 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 73 | 9563 |
| 151 and 188 | 28388 |
| 11 and 108 | 1188 |
| 124 and 192 | 5952 |
| 13 and 43 | 559 |