Least Common Multiple (LCM) of 113 and 130
The least common multiple (LCM) of 113 and 130 is 14690.
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 130?
First, calculate the GCD of 113 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 130 = 0 remainder 113 |
| 2 | 130 ÷ 113 = 1 remainder 17 |
| 3 | 113 ÷ 17 = 6 remainder 11 |
| 4 | 17 ÷ 11 = 1 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 71 | 6319 |
| 175 and 133 | 3325 |
| 71 and 113 | 8023 |
| 144 and 200 | 3600 |
| 33 and 28 | 924 |