Least Common Multiple (LCM) of 30 and 128
The least common multiple (LCM) of 30 and 128 is 1920.
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 30 and 128?
First, calculate the GCD of 30 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 128 = 0 remainder 30 |
| 2 | 128 ÷ 30 = 4 remainder 8 |
| 3 | 30 ÷ 8 = 3 remainder 6 |
| 4 | 8 ÷ 6 = 1 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 192 | 20544 |
| 55 and 198 | 990 |
| 198 and 76 | 7524 |
| 90 and 167 | 15030 |
| 106 and 54 | 2862 |