Least Common Multiple (LCM) of 102 and 31
The least common multiple (LCM) of 102 and 31 is 3162.
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 102 and 31?
First, calculate the GCD of 102 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 31 = 3 remainder 9 |
| 2 | 31 ÷ 9 = 3 remainder 4 |
| 3 | 9 ÷ 4 = 2 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 171 | 18810 |
| 157 and 85 | 13345 |
| 161 and 90 | 14490 |
| 101 and 16 | 1616 |
| 191 and 34 | 6494 |