Least Common Multiple (LCM) of 89 and 112
The least common multiple (LCM) of 89 and 112 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 89 and 112?
First, calculate the GCD of 89 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 112 = 0 remainder 89 |
| 2 | 112 ÷ 89 = 1 remainder 23 |
| 3 | 89 ÷ 23 = 3 remainder 20 |
| 4 | 23 ÷ 20 = 1 remainder 3 |
| 5 | 20 ÷ 3 = 6 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 158 | 2528 |
| 193 and 169 | 32617 |
| 10 and 118 | 590 |
| 26 and 150 | 1950 |
| 124 and 30 | 1860 |