Least Common Multiple (LCM) of 128 and 74
The least common multiple (LCM) of 128 and 74 is 4736.
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 74?
First, calculate the GCD of 128 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 74 = 1 remainder 54 |
| 2 | 74 ÷ 54 = 1 remainder 20 |
| 3 | 54 ÷ 20 = 2 remainder 14 |
| 4 | 20 ÷ 14 = 1 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 159 | 24168 |
| 151 and 150 | 22650 |
| 141 and 200 | 28200 |
| 139 and 72 | 10008 |
| 40 and 177 | 7080 |