Least Common Multiple (LCM) of 130 and 54
The least common multiple (LCM) of 130 and 54 is 3510.
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 54?
First, calculate the GCD of 130 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 54 = 2 remainder 22 |
| 2 | 54 ÷ 22 = 2 remainder 10 |
| 3 | 22 ÷ 10 = 2 remainder 2 |
| 4 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 38 | 6650 |
| 75 and 105 | 525 |
| 200 and 101 | 20200 |
| 174 and 63 | 3654 |
| 185 and 38 | 7030 |