Least Common Multiple (LCM) of 45 and 28
The least common multiple (LCM) of 45 and 28 is 1260.
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 28?
First, calculate the GCD of 45 and 28 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 28 = 1 remainder 17 |
| 2 | 28 ÷ 17 = 1 remainder 11 |
| 3 | 17 ÷ 11 = 1 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 78 | 4290 |
| 67 and 200 | 13400 |
| 198 and 152 | 15048 |
| 145 and 195 | 5655 |
| 142 and 103 | 14626 |