Least Common Multiple (LCM) of 175 and 199
The least common multiple (LCM) of 175 and 199 is 34825.
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 199?
First, calculate the GCD of 175 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 199 = 0 remainder 175 |
| 2 | 199 ÷ 175 = 1 remainder 24 |
| 3 | 175 ÷ 24 = 7 remainder 7 |
| 4 | 24 ÷ 7 = 3 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 111 | 1776 |
| 104 and 41 | 4264 |
| 108 and 156 | 1404 |
| 118 and 149 | 17582 |
| 72 and 132 | 792 |