Least Common Multiple (LCM) of 130 and 172
The least common multiple (LCM) of 130 and 172 is 11180.
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 172?
First, calculate the GCD of 130 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 172 = 0 remainder 130 |
| 2 | 172 ÷ 130 = 1 remainder 42 |
| 3 | 130 ÷ 42 = 3 remainder 4 |
| 4 | 42 ÷ 4 = 10 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 31 | 558 |
| 38 and 134 | 2546 |
| 188 and 119 | 22372 |
| 116 and 149 | 17284 |
| 60 and 20 | 60 |