Least Common Multiple (LCM) of 96 and 167
The least common multiple (LCM) of 96 and 167 is 16032.
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 167?
First, calculate the GCD of 96 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 167 = 0 remainder 96 |
| 2 | 167 ÷ 96 = 1 remainder 71 |
| 3 | 96 ÷ 71 = 1 remainder 25 |
| 4 | 71 ÷ 25 = 2 remainder 21 |
| 5 | 25 ÷ 21 = 1 remainder 4 |
| 6 | 21 ÷ 4 = 5 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 26 | 1300 |
| 12 and 105 | 420 |
| 121 and 60 | 7260 |
| 130 and 61 | 7930 |
| 50 and 52 | 1300 |