Least Common Multiple (LCM) of 189 and 104
The least common multiple (LCM) of 189 and 104 is 19656.
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 189 and 104?
First, calculate the GCD of 189 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 104 = 1 remainder 85 |
| 2 | 104 ÷ 85 = 1 remainder 19 |
| 3 | 85 ÷ 19 = 4 remainder 9 |
| 4 | 19 ÷ 9 = 2 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 176 | 6160 |
| 30 and 200 | 600 |
| 189 and 157 | 29673 |
| 45 and 72 | 360 |
| 103 and 164 | 16892 |