Least Common Multiple (LCM) of 186 and 65
The least common multiple (LCM) of 186 and 65 is 12090.
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 65?
First, calculate the GCD of 186 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 65 = 2 remainder 56 |
| 2 | 65 ÷ 56 = 1 remainder 9 |
| 3 | 56 ÷ 9 = 6 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 14 | 350 |
| 179 and 86 | 15394 |
| 170 and 44 | 3740 |
| 152 and 88 | 1672 |
| 145 and 14 | 2030 |