Least Common Multiple (LCM) of 65 and 186
The least common multiple (LCM) of 65 and 186 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 65 and 186?
First, calculate the GCD of 65 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 186 = 0 remainder 65 |
| 2 | 186 ÷ 65 = 2 remainder 56 |
| 3 | 65 ÷ 56 = 1 remainder 9 |
| 4 | 56 ÷ 9 = 6 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 175 | 4725 |
| 86 and 105 | 9030 |
| 195 and 137 | 26715 |
| 156 and 116 | 4524 |
| 117 and 162 | 2106 |