Least Common Multiple (LCM) of 144 and 78
The least common multiple (LCM) of 144 and 78 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 78?
First, calculate the GCD of 144 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 78 = 1 remainder 66 |
| 2 | 78 ÷ 66 = 1 remainder 12 |
| 3 | 66 ÷ 12 = 5 remainder 6 |
| 4 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 106 | 9752 |
| 42 and 114 | 798 |
| 148 and 158 | 11692 |
| 133 and 122 | 16226 |
| 75 and 113 | 8475 |