Least Common Multiple (LCM) of 16 and 117
The least common multiple (LCM) of 16 and 117 is 1872.
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 117?
First, calculate the GCD of 16 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 117 = 0 remainder 16 |
| 2 | 117 ÷ 16 = 7 remainder 5 |
| 3 | 16 ÷ 5 = 3 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 195 | 38805 |
| 200 and 155 | 6200 |
| 43 and 59 | 2537 |
| 104 and 195 | 1560 |
| 112 and 72 | 1008 |