Least Common Multiple (LCM) of 16 and 71
The least common multiple (LCM) of 16 and 71 is 1136.
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 71?
First, calculate the GCD of 16 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 71 = 0 remainder 16 |
| 2 | 71 ÷ 16 = 4 remainder 7 |
| 3 | 16 ÷ 7 = 2 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 169 | 12506 |
| 24 and 54 | 216 |
| 109 and 174 | 18966 |
| 25 and 144 | 3600 |
| 28 and 118 | 1652 |