Least Common Multiple (LCM) of 106 and 139
The least common multiple (LCM) of 106 and 139 is 14734.
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 139?
First, calculate the GCD of 106 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 139 = 0 remainder 106 |
| 2 | 139 ÷ 106 = 1 remainder 33 |
| 3 | 106 ÷ 33 = 3 remainder 7 |
| 4 | 33 ÷ 7 = 4 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 85 | 1785 |
| 89 and 104 | 9256 |
| 96 and 189 | 6048 |
| 140 and 182 | 1820 |
| 142 and 180 | 12780 |