Least Common Multiple (LCM) of 45 and 83
The least common multiple (LCM) of 45 and 83 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 45 and 83?
First, calculate the GCD of 45 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 83 = 0 remainder 45 |
| 2 | 83 ÷ 45 = 1 remainder 38 |
| 3 | 45 ÷ 38 = 1 remainder 7 |
| 4 | 38 ÷ 7 = 5 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 20 | 60 |
| 148 and 78 | 5772 |
| 13 and 193 | 2509 |
| 148 and 57 | 8436 |
| 106 and 185 | 19610 |