Least Common Multiple (LCM) of 130 and 198
The least common multiple (LCM) of 130 and 198 is 12870.
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 198?
First, calculate the GCD of 130 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 198 = 0 remainder 130 |
| 2 | 198 ÷ 130 = 1 remainder 68 |
| 3 | 130 ÷ 68 = 1 remainder 62 |
| 4 | 68 ÷ 62 = 1 remainder 6 |
| 5 | 62 ÷ 6 = 10 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 116 | 3944 |
| 30 and 118 | 1770 |
| 178 and 152 | 13528 |
| 15 and 78 | 390 |
| 145 and 199 | 28855 |