Least Common Multiple (LCM) of 130 and 174
The least common multiple (LCM) of 130 and 174 is 11310.
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 174?
First, calculate the GCD of 130 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 174 = 0 remainder 130 |
| 2 | 174 ÷ 130 = 1 remainder 44 |
| 3 | 130 ÷ 44 = 2 remainder 42 |
| 4 | 44 ÷ 42 = 1 remainder 2 |
| 5 | 42 ÷ 2 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 66 | 2310 |
| 186 and 137 | 25482 |
| 101 and 76 | 7676 |
| 58 and 17 | 986 |
| 129 and 122 | 15738 |