Least Common Multiple (LCM) of 31 and 90
The least common multiple (LCM) of 31 and 90 is 2790.
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 90?
First, calculate the GCD of 31 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 90 = 0 remainder 31 |
| 2 | 90 ÷ 31 = 2 remainder 28 |
| 3 | 31 ÷ 28 = 1 remainder 3 |
| 4 | 28 ÷ 3 = 9 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 51 | 255 |
| 16 and 22 | 176 |
| 175 and 90 | 3150 |
| 104 and 22 | 1144 |
| 139 and 47 | 6533 |