Least Common Multiple (LCM) of 106 and 39
The least common multiple (LCM) of 106 and 39 is 4134.
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 39?
First, calculate the GCD of 106 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 39 = 2 remainder 28 |
| 2 | 39 ÷ 28 = 1 remainder 11 |
| 3 | 28 ÷ 11 = 2 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 108 | 7884 |
| 28 and 42 | 84 |
| 75 and 56 | 4200 |
| 27 and 183 | 1647 |
| 63 and 29 | 1827 |