Least Common Multiple (LCM) of 105 and 16
The least common multiple (LCM) of 105 and 16 is 1680.
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 16?
First, calculate the GCD of 105 and 16 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 16 = 6 remainder 9 |
| 2 | 16 ÷ 9 = 1 remainder 7 |
| 3 | 9 ÷ 7 = 1 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 28 and 24 | 168 |
| 96 and 158 | 7584 |
| 104 and 188 | 4888 |
| 127 and 160 | 20320 |
| 92 and 146 | 6716 |