Least Common Multiple (LCM) of 106 and 144
The least common multiple (LCM) of 106 and 144 is 7632.
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 144?
First, calculate the GCD of 106 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 144 = 0 remainder 106 |
| 2 | 144 ÷ 106 = 1 remainder 38 |
| 3 | 106 ÷ 38 = 2 remainder 30 |
| 4 | 38 ÷ 30 = 1 remainder 8 |
| 5 | 30 ÷ 8 = 3 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 105 | 525 |
| 140 and 164 | 5740 |
| 132 and 65 | 8580 |
| 107 and 177 | 18939 |
| 102 and 77 | 7854 |