Least Common Multiple (LCM) of 77 and 144
The least common multiple (LCM) of 77 and 144 is 11088.
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 77 and 144?
First, calculate the GCD of 77 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 144 = 0 remainder 77 |
| 2 | 144 ÷ 77 = 1 remainder 67 |
| 3 | 77 ÷ 67 = 1 remainder 10 |
| 4 | 67 ÷ 10 = 6 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 49 | 3969 |
| 75 and 11 | 825 |
| 35 and 21 | 105 |
| 154 and 74 | 5698 |
| 197 and 153 | 30141 |