Least Common Multiple (LCM) of 36 and 128
The least common multiple (LCM) of 36 and 128 is 1152.
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 36 and 128?
First, calculate the GCD of 36 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 128 = 0 remainder 36 |
| 2 | 128 ÷ 36 = 3 remainder 20 |
| 3 | 36 ÷ 20 = 1 remainder 16 |
| 4 | 20 ÷ 16 = 1 remainder 4 |
| 5 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 97 | 5238 |
| 81 and 138 | 3726 |
| 47 and 133 | 6251 |
| 112 and 181 | 20272 |
| 142 and 126 | 8946 |