Least Common Multiple (LCM) of 16 and 27
The least common multiple (LCM) of 16 and 27 is 432.
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 27?
First, calculate the GCD of 16 and 27 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 27 = 0 remainder 16 |
| 2 | 27 ÷ 16 = 1 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 |
|---|---|
| 113 and 198 | 22374 |
| 44 and 177 | 7788 |
| 140 and 26 | 1820 |
| 129 and 163 | 21027 |
| 126 and 58 | 3654 |