Least Common Multiple (LCM) of 144 and 39
The least common multiple (LCM) of 144 and 39 is 1872.
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 39?
First, calculate the GCD of 144 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 39 = 3 remainder 27 |
| 2 | 39 ÷ 27 = 1 remainder 12 |
| 3 | 27 ÷ 12 = 2 remainder 3 |
| 4 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 129 | 5676 |
| 157 and 20 | 3140 |
| 167 and 114 | 19038 |
| 105 and 107 | 11235 |
| 193 and 18 | 3474 |