Least Common Multiple (LCM) of 118 and 165
The least common multiple (LCM) of 118 and 165 is 19470.
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 118 and 165?
First, calculate the GCD of 118 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 165 = 0 remainder 118 |
| 2 | 165 ÷ 118 = 1 remainder 47 |
| 3 | 118 ÷ 47 = 2 remainder 24 |
| 4 | 47 ÷ 24 = 1 remainder 23 |
| 5 | 24 ÷ 23 = 1 remainder 1 |
| 6 | 23 ÷ 1 = 23 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 24 | 984 |
| 25 and 123 | 3075 |
| 183 and 126 | 7686 |
| 47 and 21 | 987 |
| 15 and 134 | 2010 |