Least Common Multiple (LCM) of 175 and 52
The least common multiple (LCM) of 175 and 52 is 9100.
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 52?
First, calculate the GCD of 175 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 52 = 3 remainder 19 |
| 2 | 52 ÷ 19 = 2 remainder 14 |
| 3 | 19 ÷ 14 = 1 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 198 | 5742 |
| 44 and 72 | 792 |
| 109 and 65 | 7085 |
| 188 and 119 | 22372 |
| 75 and 158 | 11850 |