Least Common Multiple (LCM) of 48 and 75
The least common multiple (LCM) of 48 and 75 is 1200.
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 48 and 75?
First, calculate the GCD of 48 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 75 = 0 remainder 48 |
| 2 | 75 ÷ 48 = 1 remainder 27 |
| 3 | 48 ÷ 27 = 1 remainder 21 |
| 4 | 27 ÷ 21 = 1 remainder 6 |
| 5 | 21 ÷ 6 = 3 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 137 | 8357 |
| 71 and 105 | 7455 |
| 54 and 108 | 108 |
| 70 and 52 | 1820 |
| 160 and 152 | 3040 |