Least Common Multiple (LCM) of 54 and 125
The least common multiple (LCM) of 54 and 125 is 6750.
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 125?
First, calculate the GCD of 54 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 125 = 0 remainder 54 |
| 2 | 125 ÷ 54 = 2 remainder 17 |
| 3 | 54 ÷ 17 = 3 remainder 3 |
| 4 | 17 ÷ 3 = 5 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 17 | 1275 |
| 175 and 87 | 15225 |
| 30 and 168 | 840 |
| 153 and 127 | 19431 |
| 100 and 103 | 10300 |