Least Common Multiple (LCM) of 31 and 99
The least common multiple (LCM) of 31 and 99 is 3069.
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 99?
First, calculate the GCD of 31 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 99 = 0 remainder 31 |
| 2 | 99 ÷ 31 = 3 remainder 6 |
| 3 | 31 ÷ 6 = 5 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 173 | 27507 |
| 128 and 106 | 6784 |
| 28 and 100 | 700 |
| 27 and 76 | 2052 |
| 158 and 145 | 22910 |