Least Common Multiple (LCM) of 71 and 190
The least common multiple (LCM) of 71 and 190 is 13490.
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 190?
First, calculate the GCD of 71 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 190 = 0 remainder 71 |
| 2 | 190 ÷ 71 = 2 remainder 48 |
| 3 | 71 ÷ 48 = 1 remainder 23 |
| 4 | 48 ÷ 23 = 2 remainder 2 |
| 5 | 23 ÷ 2 = 11 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 75 | 3900 |
| 112 and 61 | 6832 |
| 77 and 74 | 5698 |
| 195 and 130 | 390 |
| 18 and 17 | 306 |