Least Common Multiple (LCM) of 172 and 192
The least common multiple (LCM) of 172 and 192 is 8256.
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 172 and 192?
First, calculate the GCD of 172 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 192 = 0 remainder 172 |
| 2 | 192 ÷ 172 = 1 remainder 20 |
| 3 | 172 ÷ 20 = 8 remainder 12 |
| 4 | 20 ÷ 12 = 1 remainder 8 |
| 5 | 12 ÷ 8 = 1 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 147 | 7497 |
| 110 and 95 | 2090 |
| 110 and 46 | 2530 |
| 106 and 176 | 9328 |
| 123 and 199 | 24477 |