Least Common Multiple (LCM) of 112 and 71
The least common multiple (LCM) of 112 and 71 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 112 and 71?
First, calculate the GCD of 112 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 71 = 1 remainder 41 |
| 2 | 71 ÷ 41 = 1 remainder 30 |
| 3 | 41 ÷ 30 = 1 remainder 11 |
| 4 | 30 ÷ 11 = 2 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 65 | 7215 |
| 177 and 72 | 4248 |
| 17 and 93 | 1581 |
| 133 and 144 | 19152 |
| 40 and 186 | 3720 |