Least Common Multiple (LCM) of 144 and 188
The least common multiple (LCM) of 144 and 188 is 6768.
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 188?
First, calculate the GCD of 144 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 188 = 0 remainder 144 |
| 2 | 188 ÷ 144 = 1 remainder 44 |
| 3 | 144 ÷ 44 = 3 remainder 12 |
| 4 | 44 ÷ 12 = 3 remainder 8 |
| 5 | 12 ÷ 8 = 1 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 31 | 3255 |
| 72 and 41 | 2952 |
| 17 and 42 | 714 |
| 119 and 20 | 2380 |
| 109 and 29 | 3161 |