Least Common Multiple (LCM) of 188 and 165
The least common multiple (LCM) of 188 and 165 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 188 and 165?
First, calculate the GCD of 188 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 165 = 1 remainder 23 |
| 2 | 165 ÷ 23 = 7 remainder 4 |
| 3 | 23 ÷ 4 = 5 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 107 | 9309 |
| 154 and 191 | 29414 |
| 94 and 152 | 7144 |
| 109 and 149 | 16241 |
| 97 and 71 | 6887 |