Least Common Multiple (LCM) of 16 and 171
The least common multiple (LCM) of 16 and 171 is 2736.
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 171?
First, calculate the GCD of 16 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 171 = 0 remainder 16 |
| 2 | 171 ÷ 16 = 10 remainder 11 |
| 3 | 16 ÷ 11 = 1 remainder 5 |
| 4 | 11 ÷ 5 = 2 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 139 | 23352 |
| 82 and 78 | 3198 |
| 102 and 140 | 7140 |
| 157 and 105 | 16485 |
| 22 and 200 | 2200 |