Least Common Multiple (LCM) of 130 and 57
The least common multiple (LCM) of 130 and 57 is 7410.
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 57?
First, calculate the GCD of 130 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 57 = 2 remainder 16 |
| 2 | 57 ÷ 16 = 3 remainder 9 |
| 3 | 16 ÷ 9 = 1 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 47 | 6110 |
| 115 and 186 | 21390 |
| 117 and 14 | 1638 |
| 71 and 70 | 4970 |
| 102 and 66 | 1122 |