Least Common Multiple (LCM) of 186 and 72
The least common multiple (LCM) of 186 and 72 is 2232.
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 186 and 72?
First, calculate the GCD of 186 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 72 = 2 remainder 42 |
| 2 | 72 ÷ 42 = 1 remainder 30 |
| 3 | 42 ÷ 30 = 1 remainder 12 |
| 4 | 30 ÷ 12 = 2 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 199 | 29850 |
| 104 and 172 | 4472 |
| 60 and 15 | 60 |
| 187 and 168 | 31416 |
| 172 and 131 | 22532 |