Least Common Multiple (LCM) of 54 and 175
The least common multiple (LCM) of 54 and 175 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 54 and 175?
First, calculate the GCD of 54 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 175 = 0 remainder 54 |
| 2 | 175 ÷ 54 = 3 remainder 13 |
| 3 | 54 ÷ 13 = 4 remainder 2 |
| 4 | 13 ÷ 2 = 6 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 26 and 55 | 1430 |
| 55 and 89 | 4895 |
| 75 and 10 | 150 |
| 11 and 33 | 33 |
| 63 and 48 | 1008 |