Least Common Multiple (LCM) of 28 and 104
The least common multiple (LCM) of 28 and 104 is 728.
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 28 and 104?
First, calculate the GCD of 28 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 28 ÷ 104 = 0 remainder 28 |
| 2 | 104 ÷ 28 = 3 remainder 20 |
| 3 | 28 ÷ 20 = 1 remainder 8 |
| 4 | 20 ÷ 8 = 2 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 57 | 7068 |
| 85 and 192 | 16320 |
| 30 and 59 | 1770 |
| 140 and 54 | 3780 |
| 145 and 184 | 26680 |