Least Common Multiple (LCM) of 162 and 106
The least common multiple (LCM) of 162 and 106 is 8586.
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 162 and 106?
First, calculate the GCD of 162 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 106 = 1 remainder 56 |
| 2 | 106 ÷ 56 = 1 remainder 50 |
| 3 | 56 ÷ 50 = 1 remainder 6 |
| 4 | 50 ÷ 6 = 8 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 41 | 1517 |
| 107 and 81 | 8667 |
| 99 and 200 | 19800 |
| 132 and 33 | 132 |
| 11 and 15 | 165 |