Least Common Multiple (LCM) of 144 and 111
The least common multiple (LCM) of 144 and 111 is 5328.
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 111?
First, calculate the GCD of 144 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 111 = 1 remainder 33 |
| 2 | 111 ÷ 33 = 3 remainder 12 |
| 3 | 33 ÷ 12 = 2 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 144 | 22608 |
| 13 and 123 | 1599 |
| 79 and 106 | 8374 |
| 144 and 104 | 1872 |
| 126 and 186 | 3906 |