Least Common Multiple (LCM) of 112 and 89
The least common multiple (LCM) of 112 and 89 is 9968.
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 89?
First, calculate the GCD of 112 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 89 = 1 remainder 23 |
| 2 | 89 ÷ 23 = 3 remainder 20 |
| 3 | 23 ÷ 20 = 1 remainder 3 |
| 4 | 20 ÷ 3 = 6 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 52 | 468 |
| 153 and 31 | 4743 |
| 49 and 19 | 931 |
| 189 and 32 | 6048 |
| 61 and 113 | 6893 |