Least Common Multiple (LCM) of 45 and 89
The least common multiple (LCM) of 45 and 89 is 4005.
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 45 and 89?
First, calculate the GCD of 45 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 89 = 0 remainder 45 |
| 2 | 89 ÷ 45 = 1 remainder 44 |
| 3 | 45 ÷ 44 = 1 remainder 1 |
| 4 | 44 ÷ 1 = 44 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 171 | 22230 |
| 123 and 33 | 1353 |
| 63 and 107 | 6741 |
| 76 and 130 | 4940 |
| 134 and 58 | 3886 |