Least Common Multiple (LCM) of 107 and 144
The least common multiple (LCM) of 107 and 144 is 15408.
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 107 and 144?
First, calculate the GCD of 107 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 144 = 0 remainder 107 |
| 2 | 144 ÷ 107 = 1 remainder 37 |
| 3 | 107 ÷ 37 = 2 remainder 33 |
| 4 | 37 ÷ 33 = 1 remainder 4 |
| 5 | 33 ÷ 4 = 8 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 101 | 15251 |
| 85 and 45 | 765 |
| 78 and 21 | 546 |
| 156 and 136 | 5304 |
| 114 and 78 | 1482 |