Least Common Multiple (LCM) of 106 and 162
The least common multiple (LCM) of 106 and 162 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 106 and 162?
First, calculate the GCD of 106 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 162 = 0 remainder 106 |
| 2 | 162 ÷ 106 = 1 remainder 56 |
| 3 | 106 ÷ 56 = 1 remainder 50 |
| 4 | 56 ÷ 50 = 1 remainder 6 |
| 5 | 50 ÷ 6 = 8 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 76 | 2964 |
| 132 and 152 | 5016 |
| 50 and 78 | 1950 |
| 175 and 21 | 525 |
| 77 and 126 | 1386 |