Least Common Multiple (LCM) of 96 and 89
The least common multiple (LCM) of 96 and 89 is 8544.
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 96 and 89?
First, calculate the GCD of 96 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 89 = 1 remainder 7 |
| 2 | 89 ÷ 7 = 12 remainder 5 |
| 3 | 7 ÷ 5 = 1 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 138 | 4278 |
| 195 and 141 | 9165 |
| 120 and 62 | 3720 |
| 17 and 67 | 1139 |
| 90 and 166 | 7470 |