Least Common Multiple (LCM) of 186 and 165
The least common multiple (LCM) of 186 and 165 is 10230.
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 165?
First, calculate the GCD of 186 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 165 = 1 remainder 21 |
| 2 | 165 ÷ 21 = 7 remainder 18 |
| 3 | 21 ÷ 18 = 1 remainder 3 |
| 4 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 45 | 4635 |
| 105 and 108 | 3780 |
| 105 and 176 | 18480 |
| 176 and 23 | 4048 |
| 58 and 35 | 2030 |