Least Common Multiple (LCM) of 105 and 104
The least common multiple (LCM) of 105 and 104 is 10920.
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 105 and 104?
First, calculate the GCD of 105 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 104 = 1 remainder 1 |
| 2 | 104 ÷ 1 = 104 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 45 | 2070 |
| 100 and 49 | 4900 |
| 159 and 80 | 12720 |
| 180 and 85 | 3060 |
| 135 and 47 | 6345 |