Least Common Multiple (LCM) of 165 and 105
The least common multiple (LCM) of 165 and 105 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 165 and 105?
First, calculate the GCD of 165 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 105 = 1 remainder 60 |
| 2 | 105 ÷ 60 = 1 remainder 45 |
| 3 | 60 ÷ 45 = 1 remainder 15 |
| 4 | 45 ÷ 15 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 70 | 700 |
| 100 and 130 | 1300 |
| 178 and 126 | 11214 |
| 60 and 176 | 2640 |
| 78 and 147 | 3822 |