Least Common Multiple (LCM) of 71 and 130
The least common multiple (LCM) of 71 and 130 is 9230.
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 71 and 130?
First, calculate the GCD of 71 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 130 = 0 remainder 71 |
| 2 | 130 ÷ 71 = 1 remainder 59 |
| 3 | 71 ÷ 59 = 1 remainder 12 |
| 4 | 59 ÷ 12 = 4 remainder 11 |
| 5 | 12 ÷ 11 = 1 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 77 | 8162 |
| 45 and 126 | 630 |
| 193 and 168 | 32424 |
| 105 and 111 | 3885 |
| 88 and 138 | 6072 |