Least Common Multiple (LCM) of 31 and 66
The least common multiple (LCM) of 31 and 66 is 2046.
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 31 and 66?
First, calculate the GCD of 31 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 66 = 0 remainder 31 |
| 2 | 66 ÷ 31 = 2 remainder 4 |
| 3 | 31 ÷ 4 = 7 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 195 | 2145 |
| 149 and 138 | 20562 |
| 91 and 163 | 14833 |
| 37 and 104 | 3848 |
| 183 and 110 | 20130 |