Least Common Multiple (LCM) of 100 and 128
The least common multiple (LCM) of 100 and 128 is 3200.
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 100 and 128?
First, calculate the GCD of 100 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 128 = 0 remainder 100 |
| 2 | 128 ÷ 100 = 1 remainder 28 |
| 3 | 100 ÷ 28 = 3 remainder 16 |
| 4 | 28 ÷ 16 = 1 remainder 12 |
| 5 | 16 ÷ 12 = 1 remainder 4 |
| 6 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 103 | 5665 |
| 84 and 137 | 11508 |
| 154 and 37 | 5698 |
| 157 and 39 | 6123 |
| 103 and 143 | 14729 |