Least Common Multiple (LCM) of 165 and 188
The least common multiple (LCM) of 165 and 188 is 31020.
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 165 and 188?
First, calculate the GCD of 165 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 188 = 0 remainder 165 |
| 2 | 188 ÷ 165 = 1 remainder 23 |
| 3 | 165 ÷ 23 = 7 remainder 4 |
| 4 | 23 ÷ 4 = 5 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 120 | 10920 |
| 195 and 197 | 38415 |
| 144 and 195 | 9360 |
| 118 and 25 | 2950 |
| 172 and 90 | 7740 |