Least Common Multiple (LCM) of 91 and 66
The least common multiple (LCM) of 91 and 66 is 6006.
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 66?
First, calculate the GCD of 91 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 66 = 1 remainder 25 |
| 2 | 66 ÷ 25 = 2 remainder 16 |
| 3 | 25 ÷ 16 = 1 remainder 9 |
| 4 | 16 ÷ 9 = 1 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 107 | 6313 |
| 129 and 159 | 6837 |
| 18 and 158 | 1422 |
| 12 and 74 | 444 |
| 27 and 171 | 513 |