Least Common Multiple (LCM) of 112 and 87
The least common multiple (LCM) of 112 and 87 is 9744.
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 87?
First, calculate the GCD of 112 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 87 = 1 remainder 25 |
| 2 | 87 ÷ 25 = 3 remainder 12 |
| 3 | 25 ÷ 12 = 2 remainder 1 |
| 4 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 41 | 41 |
| 59 and 25 | 1475 |
| 141 and 50 | 7050 |
| 16 and 68 | 272 |
| 164 and 180 | 7380 |