Least Common Multiple (LCM) of 54 and 75
The least common multiple (LCM) of 54 and 75 is 1350.
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 75?
First, calculate the GCD of 54 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 75 = 0 remainder 54 |
| 2 | 75 ÷ 54 = 1 remainder 21 |
| 3 | 54 ÷ 21 = 2 remainder 12 |
| 4 | 21 ÷ 12 = 1 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 11 | 352 |
| 100 and 81 | 8100 |
| 121 and 49 | 5929 |
| 87 and 16 | 1392 |
| 11 and 124 | 1364 |