Least Common Multiple (LCM) of 144 and 77
The least common multiple (LCM) of 144 and 77 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 144 and 77?
First, calculate the GCD of 144 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 77 = 1 remainder 67 |
| 2 | 77 ÷ 67 = 1 remainder 10 |
| 3 | 67 ÷ 10 = 6 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 58 | 5568 |
| 118 and 156 | 9204 |
| 136 and 180 | 6120 |
| 38 and 120 | 2280 |
| 10 and 181 | 1810 |