Least Common Multiple (LCM) of 71 and 112
The least common multiple (LCM) of 71 and 112 is 7952.
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 112?
First, calculate the GCD of 71 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 112 = 0 remainder 71 |
| 2 | 112 ÷ 71 = 1 remainder 41 |
| 3 | 71 ÷ 41 = 1 remainder 30 |
| 4 | 41 ÷ 30 = 1 remainder 11 |
| 5 | 30 ÷ 11 = 2 remainder 8 |
| 6 | 11 ÷ 8 = 1 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 135 | 20115 |
| 40 and 192 | 960 |
| 105 and 129 | 4515 |
| 115 and 189 | 21735 |
| 195 and 81 | 5265 |