Least Common Multiple (LCM) of 31 and 96
The least common multiple (LCM) of 31 and 96 is 2976.
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 96?
First, calculate the GCD of 31 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 96 = 0 remainder 31 |
| 2 | 96 ÷ 31 = 3 remainder 3 |
| 3 | 31 ÷ 3 = 10 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 81 | 3078 |
| 183 and 144 | 8784 |
| 133 and 80 | 10640 |
| 172 and 22 | 1892 |
| 199 and 19 | 3781 |