Least Common Multiple (LCM) of 72 and 192
The least common multiple (LCM) of 72 and 192 is 576.
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 72 and 192?
First, calculate the GCD of 72 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 192 = 0 remainder 72 |
| 2 | 192 ÷ 72 = 2 remainder 48 |
| 3 | 72 ÷ 48 = 1 remainder 24 |
| 4 | 48 ÷ 24 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 85 | 3060 |
| 78 and 47 | 3666 |
| 85 and 83 | 7055 |
| 36 and 49 | 1764 |
| 15 and 139 | 2085 |