Least Common Multiple (LCM) of 96 and 163
The least common multiple (LCM) of 96 and 163 is 15648.
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 163?
First, calculate the GCD of 96 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 163 = 0 remainder 96 |
| 2 | 163 ÷ 96 = 1 remainder 67 |
| 3 | 96 ÷ 67 = 1 remainder 29 |
| 4 | 67 ÷ 29 = 2 remainder 9 |
| 5 | 29 ÷ 9 = 3 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 60 | 2220 |
| 90 and 65 | 1170 |
| 123 and 114 | 4674 |
| 114 and 135 | 5130 |
| 176 and 79 | 13904 |