Least Common Multiple (LCM) of 45 and 2
The least common multiple (LCM) of 45 and 2 is 90.
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 2?
First, calculate the GCD of 45 and 2 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 2 = 22 remainder 1 |
| 2 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 16 | 2000 |
| 83 and 134 | 11122 |
| 126 and 68 | 4284 |
| 62 and 45 | 2790 |
| 77 and 82 | 6314 |