Least Common Multiple (LCM) of 45 and 93
The least common multiple (LCM) of 45 and 93 is 1395.
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 93?
First, calculate the GCD of 45 and 93 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 93 = 0 remainder 45 |
| 2 | 93 ÷ 45 = 2 remainder 3 |
| 3 | 45 ÷ 3 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 200 | 3600 |
| 60 and 42 | 420 |
| 40 and 104 | 520 |
| 175 and 107 | 18725 |
| 75 and 187 | 14025 |