Least Common Multiple (LCM) of 108 and 16
The least common multiple (LCM) of 108 and 16 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 108 and 16?
First, calculate the GCD of 108 and 16 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 16 = 6 remainder 12 |
| 2 | 16 ÷ 12 = 1 remainder 4 |
| 3 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 97 | 18236 |
| 148 and 14 | 1036 |
| 42 and 50 | 1050 |
| 21 and 86 | 1806 |
| 117 and 145 | 16965 |