Least Common Multiple (LCM) of 106 and 165
The least common multiple (LCM) of 106 and 165 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 106 and 165?
First, calculate the GCD of 106 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 165 = 0 remainder 106 |
| 2 | 165 ÷ 106 = 1 remainder 59 |
| 3 | 106 ÷ 59 = 1 remainder 47 |
| 4 | 59 ÷ 47 = 1 remainder 12 |
| 5 | 47 ÷ 12 = 3 remainder 11 |
| 6 | 12 ÷ 11 = 1 remainder 1 |
| 7 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 11 | 759 |
| 191 and 31 | 5921 |
| 23 and 184 | 184 |
| 29 and 143 | 4147 |
| 180 and 76 | 3420 |