Least Common Multiple (LCM) of 130 and 51
The least common multiple (LCM) of 130 and 51 is 6630.
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 51?
First, calculate the GCD of 130 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 51 = 2 remainder 28 |
| 2 | 51 ÷ 28 = 1 remainder 23 |
| 3 | 28 ÷ 23 = 1 remainder 5 |
| 4 | 23 ÷ 5 = 4 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 83 | 8881 |
| 136 and 101 | 13736 |
| 75 and 73 | 5475 |
| 106 and 136 | 7208 |
| 125 and 185 | 4625 |