Least Common Multiple (LCM) of 175 and 54
The least common multiple (LCM) of 175 and 54 is 9450.
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 54?
First, calculate the GCD of 175 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 54 = 3 remainder 13 |
| 2 | 54 ÷ 13 = 4 remainder 2 |
| 3 | 13 ÷ 2 = 6 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 60 | 7980 |
| 58 and 18 | 522 |
| 144 and 40 | 720 |
| 37 and 65 | 2405 |
| 136 and 127 | 17272 |