Least Common Multiple (LCM) of 114 and 165
The least common multiple (LCM) of 114 and 165 is 6270.
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 114 and 165?
First, calculate the GCD of 114 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 165 = 0 remainder 114 |
| 2 | 165 ÷ 114 = 1 remainder 51 |
| 3 | 114 ÷ 51 = 2 remainder 12 |
| 4 | 51 ÷ 12 = 4 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 184 | 552 |
| 181 and 123 | 22263 |
| 61 and 14 | 854 |
| 11 and 145 | 1595 |
| 85 and 162 | 13770 |