Least Common Multiple (LCM) of 130 and 163
The least common multiple (LCM) of 130 and 163 is 21190.
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 130 and 163?
First, calculate the GCD of 130 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 163 = 0 remainder 130 |
| 2 | 163 ÷ 130 = 1 remainder 33 |
| 3 | 130 ÷ 33 = 3 remainder 31 |
| 4 | 33 ÷ 31 = 1 remainder 2 |
| 5 | 31 ÷ 2 = 15 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 77 | 13706 |
| 94 and 189 | 17766 |
| 52 and 123 | 6396 |
| 153 and 51 | 153 |
| 31 and 10 | 310 |