Least Common Multiple (LCM) of 116 and 175
The least common multiple (LCM) of 116 and 175 is 20300.
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 116 and 175?
First, calculate the GCD of 116 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 175 = 0 remainder 116 |
| 2 | 175 ÷ 116 = 1 remainder 59 |
| 3 | 116 ÷ 59 = 1 remainder 57 |
| 4 | 59 ÷ 57 = 1 remainder 2 |
| 5 | 57 ÷ 2 = 28 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 37 | 1406 |
| 22 and 159 | 3498 |
| 178 and 188 | 16732 |
| 128 and 20 | 640 |
| 112 and 62 | 3472 |