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 |
|---|---|
| 10 and 132 | 660 |
| 79 and 57 | 4503 |
| 91 and 128 | 11648 |
| 132 and 107 | 14124 |
| 11 and 109 | 1199 |