Least Common Multiple (LCM) of 83 and 45
The least common multiple (LCM) of 83 and 45 is 3735.
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 83 and 45?
First, calculate the GCD of 83 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 45 = 1 remainder 38 |
| 2 | 45 ÷ 38 = 1 remainder 7 |
| 3 | 38 ÷ 7 = 5 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 115 | 3105 |
| 97 and 95 | 9215 |
| 193 and 84 | 16212 |
| 149 and 73 | 10877 |
| 36 and 25 | 900 |