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 |
|---|---|
| 175 and 174 | 30450 |
| 56 and 77 | 616 |
| 31 and 52 | 1612 |
| 41 and 143 | 5863 |
| 130 and 116 | 7540 |