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 |
|---|---|
| 141 and 162 | 7614 |
| 62 and 16 | 496 |
| 80 and 186 | 7440 |
| 188 and 11 | 2068 |
| 157 and 33 | 5181 |