Least Common Multiple (LCM) of 83 and 175
The least common multiple (LCM) of 83 and 175 is 14525.
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 83 and 175?
First, calculate the GCD of 83 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 175 = 0 remainder 83 |
| 2 | 175 ÷ 83 = 2 remainder 9 |
| 3 | 83 ÷ 9 = 9 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 177 | 8142 |
| 66 and 88 | 264 |
| 194 and 21 | 4074 |
| 66 and 158 | 5214 |
| 21 and 57 | 399 |