Least Common Multiple (LCM) of 96 and 171
The least common multiple (LCM) of 96 and 171 is 5472.
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 171?
First, calculate the GCD of 96 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 171 = 0 remainder 96 |
| 2 | 171 ÷ 96 = 1 remainder 75 |
| 3 | 96 ÷ 75 = 1 remainder 21 |
| 4 | 75 ÷ 21 = 3 remainder 12 |
| 5 | 21 ÷ 12 = 1 remainder 9 |
| 6 | 12 ÷ 9 = 1 remainder 3 |
| 7 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 44 and 149 | 6556 |
| 133 and 183 | 24339 |
| 44 and 145 | 6380 |
| 84 and 126 | 252 |
| 68 and 189 | 12852 |