Least Common Multiple (LCM) of 16 and 56
The least common multiple (LCM) of 16 and 56 is 112.
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 56?
First, calculate the GCD of 16 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 56 = 0 remainder 16 |
| 2 | 56 ÷ 16 = 3 remainder 8 |
| 3 | 16 ÷ 8 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 123 | 19434 |
| 152 and 198 | 15048 |
| 117 and 57 | 2223 |
| 118 and 61 | 7198 |
| 163 and 154 | 25102 |