Least Common Multiple (LCM) of 167 and 192
The least common multiple (LCM) of 167 and 192 is 32064.
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 192?
First, calculate the GCD of 167 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 192 = 0 remainder 167 |
| 2 | 192 ÷ 167 = 1 remainder 25 |
| 3 | 167 ÷ 25 = 6 remainder 17 |
| 4 | 25 ÷ 17 = 1 remainder 8 |
| 5 | 17 ÷ 8 = 2 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 192 | 2112 |
| 47 and 97 | 4559 |
| 120 and 144 | 720 |
| 131 and 61 | 7991 |
| 117 and 132 | 5148 |