Least Common Multiple (LCM) of 167 and 96
The least common multiple (LCM) of 167 and 96 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 167 and 96?
First, calculate the GCD of 167 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 96 = 1 remainder 71 |
| 2 | 96 ÷ 71 = 1 remainder 25 |
| 3 | 71 ÷ 25 = 2 remainder 21 |
| 4 | 25 ÷ 21 = 1 remainder 4 |
| 5 | 21 ÷ 4 = 5 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 69 | 4347 |
| 107 and 100 | 10700 |
| 198 and 70 | 6930 |
| 149 and 97 | 14453 |
| 15 and 155 | 465 |