Least Common Multiple (LCM) of 89 and 143
The least common multiple (LCM) of 89 and 143 is 12727.
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 143?
First, calculate the GCD of 89 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 143 = 0 remainder 89 |
| 2 | 143 ÷ 89 = 1 remainder 54 |
| 3 | 89 ÷ 54 = 1 remainder 35 |
| 4 | 54 ÷ 35 = 1 remainder 19 |
| 5 | 35 ÷ 19 = 1 remainder 16 |
| 6 | 19 ÷ 16 = 1 remainder 3 |
| 7 | 16 ÷ 3 = 5 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 117 | 4680 |
| 72 and 43 | 3096 |
| 54 and 173 | 9342 |
| 16 and 52 | 208 |
| 193 and 42 | 8106 |