Least Common Multiple (LCM) of 144 and 107
The least common multiple (LCM) of 144 and 107 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 144 and 107?
First, calculate the GCD of 144 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 107 = 1 remainder 37 |
| 2 | 107 ÷ 37 = 2 remainder 33 |
| 3 | 37 ÷ 33 = 1 remainder 4 |
| 4 | 33 ÷ 4 = 8 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 118 | 3422 |
| 21 and 199 | 4179 |
| 118 and 132 | 7788 |
| 113 and 172 | 19436 |
| 21 and 189 | 189 |