Least Common Multiple (LCM) of 113 and 45
The least common multiple (LCM) of 113 and 45 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 113 and 45?
First, calculate the GCD of 113 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 45 = 2 remainder 23 |
| 2 | 45 ÷ 23 = 1 remainder 22 |
| 3 | 23 ÷ 22 = 1 remainder 1 |
| 4 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 193 | 13510 |
| 122 and 86 | 5246 |
| 67 and 21 | 1407 |
| 141 and 10 | 1410 |
| 72 and 55 | 3960 |