Least Common Multiple (LCM) of 45 and 58
The least common multiple (LCM) of 45 and 58 is 2610.
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 58?
First, calculate the GCD of 45 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 58 = 0 remainder 45 |
| 2 | 58 ÷ 45 = 1 remainder 13 |
| 3 | 45 ÷ 13 = 3 remainder 6 |
| 4 | 13 ÷ 6 = 2 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 155 | 11935 |
| 89 and 194 | 17266 |
| 193 and 94 | 18142 |
| 157 and 118 | 18526 |
| 28 and 198 | 2772 |