Least Common Multiple (LCM) of 111 and 144
The least common multiple (LCM) of 111 and 144 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 111 and 144?
First, calculate the GCD of 111 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 144 = 0 remainder 111 |
| 2 | 144 ÷ 111 = 1 remainder 33 |
| 3 | 111 ÷ 33 = 3 remainder 12 |
| 4 | 33 ÷ 12 = 2 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 129 | 25026 |
| 19 and 179 | 3401 |
| 165 and 88 | 1320 |
| 165 and 63 | 3465 |
| 108 and 167 | 18036 |