Least Common Multiple (LCM) of 165 and 106
The least common multiple (LCM) of 165 and 106 is 17490.
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 106?
First, calculate the GCD of 165 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 106 = 1 remainder 59 |
| 2 | 106 ÷ 59 = 1 remainder 47 |
| 3 | 59 ÷ 47 = 1 remainder 12 |
| 4 | 47 ÷ 12 = 3 remainder 11 |
| 5 | 12 ÷ 11 = 1 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 136 | 680 |
| 63 and 35 | 315 |
| 114 and 159 | 6042 |
| 189 and 13 | 2457 |
| 117 and 64 | 7488 |