Least Common Multiple (LCM) of 44 and 189
The least common multiple (LCM) of 44 and 189 is 8316.
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 44 and 189?
First, calculate the GCD of 44 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 44 ÷ 189 = 0 remainder 44 |
| 2 | 189 ÷ 44 = 4 remainder 13 |
| 3 | 44 ÷ 13 = 3 remainder 5 |
| 4 | 13 ÷ 5 = 2 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 188 | 12220 |
| 125 and 108 | 13500 |
| 42 and 117 | 1638 |
| 86 and 33 | 2838 |
| 11 and 176 | 176 |