Least Common Multiple (LCM) of 91 and 128
The least common multiple (LCM) of 91 and 128 is 11648.
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 91 and 128?
First, calculate the GCD of 91 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 128 = 0 remainder 91 |
| 2 | 128 ÷ 91 = 1 remainder 37 |
| 3 | 91 ÷ 37 = 2 remainder 17 |
| 4 | 37 ÷ 17 = 2 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 67 | 7839 |
| 79 and 134 | 10586 |
| 29 and 179 | 5191 |
| 65 and 181 | 11765 |
| 51 and 102 | 102 |