Least Common Multiple (LCM) of 113 and 44
The least common multiple (LCM) of 113 and 44 is 4972.
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 44?
First, calculate the GCD of 113 and 44 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 44 = 2 remainder 25 |
| 2 | 44 ÷ 25 = 1 remainder 19 |
| 3 | 25 ÷ 19 = 1 remainder 6 |
| 4 | 19 ÷ 6 = 3 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 100 | 2400 |
| 198 and 107 | 21186 |
| 67 and 13 | 871 |
| 107 and 188 | 20116 |
| 191 and 79 | 15089 |