Least Common Multiple (LCM) of 75 and 192
The least common multiple (LCM) of 75 and 192 is 4800.
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 75 and 192?
First, calculate the GCD of 75 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 192 = 0 remainder 75 |
| 2 | 192 ÷ 75 = 2 remainder 42 |
| 3 | 75 ÷ 42 = 1 remainder 33 |
| 4 | 42 ÷ 33 = 1 remainder 9 |
| 5 | 33 ÷ 9 = 3 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 45 | 5040 |
| 12 and 74 | 444 |
| 170 and 35 | 1190 |
| 194 and 47 | 9118 |
| 101 and 37 | 3737 |