Least Common Multiple (LCM) of 31 and 100
The least common multiple (LCM) of 31 and 100 is 3100.
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 100?
First, calculate the GCD of 31 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 100 = 0 remainder 31 |
| 2 | 100 ÷ 31 = 3 remainder 7 |
| 3 | 31 ÷ 7 = 4 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 111 | 3996 |
| 92 and 111 | 10212 |
| 181 and 140 | 25340 |
| 43 and 89 | 3827 |
| 24 and 80 | 240 |