Least Common Multiple (LCM) of 78 and 144
The least common multiple (LCM) of 78 and 144 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 78 and 144?
First, calculate the GCD of 78 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 144 = 0 remainder 78 |
| 2 | 144 ÷ 78 = 1 remainder 66 |
| 3 | 78 ÷ 66 = 1 remainder 12 |
| 4 | 66 ÷ 12 = 5 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 42 | 462 |
| 113 and 110 | 12430 |
| 53 and 105 | 5565 |
| 177 and 92 | 16284 |
| 102 and 67 | 6834 |