Least Common Multiple (LCM) of 102 and 130
The least common multiple (LCM) of 102 and 130 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 102 and 130?
First, calculate the GCD of 102 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 130 = 0 remainder 102 |
| 2 | 130 ÷ 102 = 1 remainder 28 |
| 3 | 102 ÷ 28 = 3 remainder 18 |
| 4 | 28 ÷ 18 = 1 remainder 10 |
| 5 | 18 ÷ 10 = 1 remainder 8 |
| 6 | 10 ÷ 8 = 1 remainder 2 |
| 7 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 140 | 700 |
| 107 and 60 | 6420 |
| 183 and 106 | 19398 |
| 30 and 147 | 1470 |
| 187 and 27 | 5049 |