Least Common Multiple (LCM) of 130 and 144
The least common multiple (LCM) of 130 and 144 is 9360.
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 144?
First, calculate the GCD of 130 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 144 = 0 remainder 130 |
| 2 | 144 ÷ 130 = 1 remainder 14 |
| 3 | 130 ÷ 14 = 9 remainder 4 |
| 4 | 14 ÷ 4 = 3 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 32 | 64 |
| 21 and 31 | 651 |
| 186 and 70 | 6510 |
| 49 and 65 | 3185 |
| 114 and 177 | 6726 |