Least Common Multiple (LCM) of 16 and 102
The least common multiple (LCM) of 16 and 102 is 816.
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 16 and 102?
First, calculate the GCD of 16 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 102 = 0 remainder 16 |
| 2 | 102 ÷ 16 = 6 remainder 6 |
| 3 | 16 ÷ 6 = 2 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 128 | 18304 |
| 83 and 160 | 13280 |
| 106 and 116 | 6148 |
| 169 and 26 | 338 |
| 137 and 71 | 9727 |