Least Common Multiple (LCM) of 105 and 71
The least common multiple (LCM) of 105 and 71 is 7455.
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 105 and 71?
First, calculate the GCD of 105 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 71 = 1 remainder 34 |
| 2 | 71 ÷ 34 = 2 remainder 3 |
| 3 | 34 ÷ 3 = 11 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 195 | 585 |
| 116 and 97 | 11252 |
| 140 and 101 | 14140 |
| 140 and 200 | 1400 |
| 172 and 198 | 17028 |