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 |
|---|---|
| 189 and 172 | 32508 |
| 138 and 62 | 4278 |
| 142 and 170 | 12070 |
| 146 and 93 | 13578 |
| 130 and 98 | 6370 |