Least Common Multiple (LCM) of 45 and 23
The least common multiple (LCM) of 45 and 23 is 1035.
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 23?
First, calculate the GCD of 45 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 23 = 1 remainder 22 |
| 2 | 23 ÷ 22 = 1 remainder 1 |
| 3 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 51 | 714 |
| 25 and 71 | 1775 |
| 12 and 34 | 204 |
| 19 and 15 | 285 |
| 66 and 31 | 2046 |