Least Common Multiple (LCM) of 84 and 128
The least common multiple (LCM) of 84 and 128 is 2688.
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 84 and 128?
First, calculate the GCD of 84 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 128 = 0 remainder 84 |
| 2 | 128 ÷ 84 = 1 remainder 44 |
| 3 | 84 ÷ 44 = 1 remainder 40 |
| 4 | 44 ÷ 40 = 1 remainder 4 |
| 5 | 40 ÷ 4 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 128 | 3456 |
| 151 and 90 | 13590 |
| 92 and 152 | 3496 |
| 181 and 13 | 2353 |
| 185 and 167 | 30895 |