Least Common Multiple (LCM) of 105 and 165
The least common multiple (LCM) of 105 and 165 is 1155.
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 105 and 165?
First, calculate the GCD of 105 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 165 = 0 remainder 105 |
| 2 | 165 ÷ 105 = 1 remainder 60 |
| 3 | 105 ÷ 60 = 1 remainder 45 |
| 4 | 60 ÷ 45 = 1 remainder 15 |
| 5 | 45 ÷ 15 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 158 | 20382 |
| 74 and 199 | 14726 |
| 67 and 74 | 4958 |
| 18 and 19 | 342 |
| 162 and 158 | 12798 |