Least Common Multiple (LCM) of 130 and 164
The least common multiple (LCM) of 130 and 164 is 10660.
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 164?
First, calculate the GCD of 130 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 164 = 0 remainder 130 |
| 2 | 164 ÷ 130 = 1 remainder 34 |
| 3 | 130 ÷ 34 = 3 remainder 28 |
| 4 | 34 ÷ 28 = 1 remainder 6 |
| 5 | 28 ÷ 6 = 4 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 138 | 21666 |
| 20 and 123 | 2460 |
| 130 and 167 | 21710 |
| 19 and 100 | 1900 |
| 154 and 71 | 10934 |