Least Common Multiple (LCM) of 106 and 182
The least common multiple (LCM) of 106 and 182 is 9646.
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 182?
First, calculate the GCD of 106 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 182 = 0 remainder 106 |
| 2 | 182 ÷ 106 = 1 remainder 76 |
| 3 | 106 ÷ 76 = 1 remainder 30 |
| 4 | 76 ÷ 30 = 2 remainder 16 |
| 5 | 30 ÷ 16 = 1 remainder 14 |
| 6 | 16 ÷ 14 = 1 remainder 2 |
| 7 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 67 | 8844 |
| 108 and 77 | 8316 |
| 34 and 100 | 1700 |
| 103 and 195 | 20085 |
| 114 and 116 | 6612 |