Least Common Multiple (LCM) of 112 and 130
The least common multiple (LCM) of 112 and 130 is 7280.
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 112 and 130?
First, calculate the GCD of 112 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 130 = 0 remainder 112 |
| 2 | 130 ÷ 112 = 1 remainder 18 |
| 3 | 112 ÷ 18 = 6 remainder 4 |
| 4 | 18 ÷ 4 = 4 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 114 | 4218 |
| 103 and 77 | 7931 |
| 110 and 59 | 6490 |
| 50 and 81 | 4050 |
| 22 and 173 | 3806 |