Least Common Multiple (LCM) of 145 and 89
The least common multiple (LCM) of 145 and 89 is 12905.
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 145 and 89?
First, calculate the GCD of 145 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 89 = 1 remainder 56 |
| 2 | 89 ÷ 56 = 1 remainder 33 |
| 3 | 56 ÷ 33 = 1 remainder 23 |
| 4 | 33 ÷ 23 = 1 remainder 10 |
| 5 | 23 ÷ 10 = 2 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 70 | 70 |
| 184 and 145 | 26680 |
| 174 and 124 | 10788 |
| 138 and 142 | 9798 |
| 194 and 149 | 28906 |