Least Common Multiple (LCM) of 53 and 130
The least common multiple (LCM) of 53 and 130 is 6890.
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 53 and 130?
First, calculate the GCD of 53 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 130 = 0 remainder 53 |
| 2 | 130 ÷ 53 = 2 remainder 24 |
| 3 | 53 ÷ 24 = 2 remainder 5 |
| 4 | 24 ÷ 5 = 4 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 129 | 129 |
| 193 and 88 | 16984 |
| 172 and 180 | 7740 |
| 11 and 10 | 110 |
| 67 and 116 | 7772 |