Least Common Multiple (LCM) of 30 and 130
The least common multiple (LCM) of 30 and 130 is 390.
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 30 and 130?
First, calculate the GCD of 30 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 130 = 0 remainder 30 |
| 2 | 130 ÷ 30 = 4 remainder 10 |
| 3 | 30 ÷ 10 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 66 | 4818 |
| 100 and 73 | 7300 |
| 35 and 60 | 420 |
| 57 and 117 | 2223 |
| 27 and 128 | 3456 |