Least Common Multiple (LCM) of 144 and 38
The least common multiple (LCM) of 144 and 38 is 2736.
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 38?
First, calculate the GCD of 144 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 38 = 3 remainder 30 |
| 2 | 38 ÷ 30 = 1 remainder 8 |
| 3 | 30 ÷ 8 = 3 remainder 6 |
| 4 | 8 ÷ 6 = 1 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 146 | 12556 |
| 110 and 72 | 3960 |
| 119 and 71 | 8449 |
| 104 and 19 | 1976 |
| 90 and 65 | 1170 |