Least Common Multiple (LCM) of 66 and 91
The least common multiple (LCM) of 66 and 91 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 66 and 91?
First, calculate the GCD of 66 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 91 = 0 remainder 66 |
| 2 | 91 ÷ 66 = 1 remainder 25 |
| 3 | 66 ÷ 25 = 2 remainder 16 |
| 4 | 25 ÷ 16 = 1 remainder 9 |
| 5 | 16 ÷ 9 = 1 remainder 7 |
| 6 | 9 ÷ 7 = 1 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 186 | 186 |
| 68 and 130 | 4420 |
| 113 and 114 | 12882 |
| 19 and 155 | 2945 |
| 107 and 135 | 14445 |