Least Common Multiple (LCM) of 128 and 42
The least common multiple (LCM) of 128 and 42 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 128 and 42?
First, calculate the GCD of 128 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 42 = 3 remainder 2 |
| 2 | 42 ÷ 2 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 107 | 11663 |
| 36 and 119 | 4284 |
| 104 and 135 | 14040 |
| 34 and 72 | 1224 |
| 153 and 50 | 7650 |