Least Common Multiple (LCM) of 16 and 175
The least common multiple (LCM) of 16 and 175 is 2800.
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 175?
First, calculate the GCD of 16 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 175 = 0 remainder 16 |
| 2 | 175 ÷ 16 = 10 remainder 15 |
| 3 | 16 ÷ 15 = 1 remainder 1 |
| 4 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 83 | 9296 |
| 102 and 154 | 7854 |
| 148 and 105 | 15540 |
| 49 and 125 | 6125 |
| 155 and 22 | 3410 |