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 |
|---|---|
| 122 and 173 | 21106 |
| 31 and 169 | 5239 |
| 89 and 27 | 2403 |
| 129 and 93 | 3999 |
| 133 and 41 | 5453 |