Least Common Multiple (LCM) of 96 and 166
The least common multiple (LCM) of 96 and 166 is 7968.
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 166?
First, calculate the GCD of 96 and 166 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 166 = 0 remainder 96 |
| 2 | 166 ÷ 96 = 1 remainder 70 |
| 3 | 96 ÷ 70 = 1 remainder 26 |
| 4 | 70 ÷ 26 = 2 remainder 18 |
| 5 | 26 ÷ 18 = 1 remainder 8 |
| 6 | 18 ÷ 8 = 2 remainder 2 |
| 7 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 105 | 3360 |
| 112 and 12 | 336 |
| 181 and 46 | 8326 |
| 21 and 26 | 546 |
| 34 and 16 | 272 |