Least Common Multiple (LCM) of 175 and 192
The least common multiple (LCM) of 175 and 192 is 33600.
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 175 and 192?
First, calculate the GCD of 175 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 192 = 0 remainder 175 |
| 2 | 192 ÷ 175 = 1 remainder 17 |
| 3 | 175 ÷ 17 = 10 remainder 5 |
| 4 | 17 ÷ 5 = 3 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 41 | 3280 |
| 102 and 151 | 15402 |
| 117 and 115 | 13455 |
| 121 and 155 | 18755 |
| 163 and 65 | 10595 |