Least Common Multiple (LCM) of 55 and 130
The least common multiple (LCM) of 55 and 130 is 1430.
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 55 and 130?
First, calculate the GCD of 55 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 130 = 0 remainder 55 |
| 2 | 130 ÷ 55 = 2 remainder 20 |
| 3 | 55 ÷ 20 = 2 remainder 15 |
| 4 | 20 ÷ 15 = 1 remainder 5 |
| 5 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 28 | 364 |
| 54 and 165 | 2970 |
| 155 and 190 | 5890 |
| 117 and 157 | 18369 |
| 125 and 43 | 5375 |