Least Common Multiple (LCM) of 130 and 168
The least common multiple (LCM) of 130 and 168 is 10920.
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 168?
First, calculate the GCD of 130 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 168 = 0 remainder 130 |
| 2 | 168 ÷ 130 = 1 remainder 38 |
| 3 | 130 ÷ 38 = 3 remainder 16 |
| 4 | 38 ÷ 16 = 2 remainder 6 |
| 5 | 16 ÷ 6 = 2 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 100 | 600 |
| 160 and 166 | 13280 |
| 177 and 160 | 28320 |
| 180 and 173 | 31140 |
| 122 and 163 | 19886 |