Least Common Multiple (LCM) of 175 and 194
The least common multiple (LCM) of 175 and 194 is 33950.
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 194?
First, calculate the GCD of 175 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 194 = 0 remainder 175 |
| 2 | 194 ÷ 175 = 1 remainder 19 |
| 3 | 175 ÷ 19 = 9 remainder 4 |
| 4 | 19 ÷ 4 = 4 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 93 and 109 | 10137 |
| 45 and 90 | 90 |
| 98 and 15 | 1470 |
| 65 and 177 | 11505 |
| 124 and 141 | 17484 |