Least Common Multiple (LCM) of 175 and 116
The least common multiple (LCM) of 175 and 116 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 175 and 116?
First, calculate the GCD of 175 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 116 = 1 remainder 59 |
| 2 | 116 ÷ 59 = 1 remainder 57 |
| 3 | 59 ÷ 57 = 1 remainder 2 |
| 4 | 57 ÷ 2 = 28 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 19 | 2565 |
| 104 and 79 | 8216 |
| 133 and 65 | 8645 |
| 57 and 56 | 3192 |
| 116 and 52 | 1508 |