Least Common Multiple (LCM) of 163 and 96
The least common multiple (LCM) of 163 and 96 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 163 and 96?
First, calculate the GCD of 163 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 96 = 1 remainder 67 |
| 2 | 96 ÷ 67 = 1 remainder 29 |
| 3 | 67 ÷ 29 = 2 remainder 9 |
| 4 | 29 ÷ 9 = 3 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 21 | 546 |
| 108 and 68 | 1836 |
| 105 and 17 | 1785 |
| 83 and 48 | 3984 |
| 72 and 176 | 1584 |