Least Common Multiple (LCM) of 100 and 31
The least common multiple (LCM) of 100 and 31 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 100 and 31?
First, calculate the GCD of 100 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 31 = 3 remainder 7 |
| 2 | 31 ÷ 7 = 4 remainder 3 |
| 3 | 7 ÷ 3 = 2 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 160 | 800 |
| 159 and 139 | 22101 |
| 200 and 63 | 12600 |
| 174 and 66 | 1914 |
| 95 and 200 | 3800 |