Least Common Multiple (LCM) of 89 and 23
The least common multiple (LCM) of 89 and 23 is 2047.
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 23?
First, calculate the GCD of 89 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 23 = 3 remainder 20 |
| 2 | 23 ÷ 20 = 1 remainder 3 |
| 3 | 20 ÷ 3 = 6 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 60 | 660 |
| 74 and 103 | 7622 |
| 105 and 105 | 105 |
| 71 and 156 | 11076 |
| 94 and 189 | 17766 |