Least Common Multiple (LCM) of 104 and 189
The least common multiple (LCM) of 104 and 189 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 104 and 189?
First, calculate the GCD of 104 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 189 = 0 remainder 104 |
| 2 | 189 ÷ 104 = 1 remainder 85 |
| 3 | 104 ÷ 85 = 1 remainder 19 |
| 4 | 85 ÷ 19 = 4 remainder 9 |
| 5 | 19 ÷ 9 = 2 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 112 | 1232 |
| 25 and 109 | 2725 |
| 18 and 151 | 2718 |
| 51 and 145 | 7395 |
| 161 and 143 | 23023 |