Least Common Multiple (LCM) of 31 and 85
The least common multiple (LCM) of 31 and 85 is 2635.
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 85?
First, calculate the GCD of 31 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 85 = 0 remainder 31 |
| 2 | 85 ÷ 31 = 2 remainder 23 |
| 3 | 31 ÷ 23 = 1 remainder 8 |
| 4 | 23 ÷ 8 = 2 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 118 | 7434 |
| 24 and 197 | 4728 |
| 21 and 143 | 3003 |
| 189 and 15 | 945 |
| 82 and 32 | 1312 |