Least Common Multiple (LCM) of 128 and 35
The least common multiple (LCM) of 128 and 35 is 4480.
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 35?
First, calculate the GCD of 128 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 35 = 3 remainder 23 |
| 2 | 35 ÷ 23 = 1 remainder 12 |
| 3 | 23 ÷ 12 = 1 remainder 11 |
| 4 | 12 ÷ 11 = 1 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 111 | 3108 |
| 113 and 129 | 14577 |
| 14 and 51 | 714 |
| 162 and 127 | 20574 |
| 22 and 152 | 1672 |