Least Common Multiple (LCM) of 128 and 53
The least common multiple (LCM) of 128 and 53 is 6784.
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 128 and 53?
First, calculate the GCD of 128 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 53 = 2 remainder 22 |
| 2 | 53 ÷ 22 = 2 remainder 9 |
| 3 | 22 ÷ 9 = 2 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 172 | 6364 |
| 172 and 77 | 13244 |
| 126 and 38 | 2394 |
| 77 and 21 | 231 |
| 110 and 104 | 5720 |