Least Common Multiple (LCM) of 165 and 101
The least common multiple (LCM) of 165 and 101 is 16665.
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 101?
First, calculate the GCD of 165 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 101 = 1 remainder 64 |
| 2 | 101 ÷ 64 = 1 remainder 37 |
| 3 | 64 ÷ 37 = 1 remainder 27 |
| 4 | 37 ÷ 27 = 1 remainder 10 |
| 5 | 27 ÷ 10 = 2 remainder 7 |
| 6 | 10 ÷ 7 = 1 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 146 | 2482 |
| 60 and 152 | 2280 |
| 135 and 21 | 945 |
| 146 and 65 | 9490 |
| 85 and 170 | 170 |