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 |
|---|---|
| 28 and 92 | 644 |
| 154 and 35 | 770 |
| 72 and 71 | 5112 |
| 113 and 108 | 12204 |
| 46 and 116 | 2668 |