Least Common Multiple (LCM) of 30 and 104
The least common multiple (LCM) of 30 and 104 is 1560.
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 30 and 104?
First, calculate the GCD of 30 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 104 = 0 remainder 30 |
| 2 | 104 ÷ 30 = 3 remainder 14 |
| 3 | 30 ÷ 14 = 2 remainder 2 |
| 4 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 93 | 3255 |
| 181 and 185 | 33485 |
| 129 and 22 | 2838 |
| 164 and 89 | 14596 |
| 146 and 160 | 11680 |