Least Common Multiple (LCM) of 45 and 113
The least common multiple (LCM) of 45 and 113 is 5085.
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 113?
First, calculate the GCD of 45 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 113 = 0 remainder 45 |
| 2 | 113 ÷ 45 = 2 remainder 23 |
| 3 | 45 ÷ 23 = 1 remainder 22 |
| 4 | 23 ÷ 22 = 1 remainder 1 |
| 5 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 177 | 11151 |
| 193 and 29 | 5597 |
| 124 and 186 | 372 |
| 42 and 167 | 7014 |
| 25 and 22 | 550 |