Least Common Multiple (LCM) of 48 and 133
The least common multiple (LCM) of 48 and 133 is 6384.
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 133?
First, calculate the GCD of 48 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 133 = 0 remainder 48 |
| 2 | 133 ÷ 48 = 2 remainder 37 |
| 3 | 48 ÷ 37 = 1 remainder 11 |
| 4 | 37 ÷ 11 = 3 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 13 | 741 |
| 111 and 200 | 22200 |
| 43 and 56 | 2408 |
| 193 and 107 | 20651 |
| 190 and 10 | 190 |