Least Common Multiple (LCM) of 113 and 80
The least common multiple (LCM) of 113 and 80 is 9040.
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 80?
First, calculate the GCD of 113 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 80 = 1 remainder 33 |
| 2 | 80 ÷ 33 = 2 remainder 14 |
| 3 | 33 ÷ 14 = 2 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 35 | 2310 |
| 33 and 29 | 957 |
| 25 and 19 | 475 |
| 127 and 77 | 9779 |
| 142 and 190 | 13490 |