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 |
|---|---|
| 14 and 93 | 1302 |
| 17 and 19 | 323 |
| 134 and 175 | 23450 |
| 136 and 59 | 8024 |
| 200 and 51 | 10200 |