Least Common Multiple (LCM) of 28 and 105
The least common multiple (LCM) of 28 and 105 is 420.
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 105?
First, calculate the GCD of 28 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 28 ÷ 105 = 0 remainder 28 |
| 2 | 105 ÷ 28 = 3 remainder 21 |
| 3 | 28 ÷ 21 = 1 remainder 7 |
| 4 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 158 | 13904 |
| 151 and 79 | 11929 |
| 114 and 32 | 1824 |
| 185 and 111 | 555 |
| 101 and 91 | 9191 |