Least Common Multiple (LCM) of 73 and 192
The least common multiple (LCM) of 73 and 192 is 14016.
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 73 and 192?
First, calculate the GCD of 73 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 192 = 0 remainder 73 |
| 2 | 192 ÷ 73 = 2 remainder 46 |
| 3 | 73 ÷ 46 = 1 remainder 27 |
| 4 | 46 ÷ 27 = 1 remainder 19 |
| 5 | 27 ÷ 19 = 1 remainder 8 |
| 6 | 19 ÷ 8 = 2 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 30 | 5790 |
| 183 and 140 | 25620 |
| 90 and 179 | 16110 |
| 113 and 96 | 10848 |
| 145 and 126 | 18270 |