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 |
|---|---|
| 67 and 47 | 3149 |
| 12 and 165 | 660 |
| 154 and 26 | 2002 |
| 175 and 132 | 23100 |
| 52 and 132 | 1716 |