Least Common Multiple (LCM) of 31 and 200
The least common multiple (LCM) of 31 and 200 is 6200.
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 200?
First, calculate the GCD of 31 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 200 = 0 remainder 31 |
| 2 | 200 ÷ 31 = 6 remainder 14 |
| 3 | 31 ÷ 14 = 2 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 140 | 7140 |
| 36 and 170 | 3060 |
| 119 and 47 | 5593 |
| 10 and 171 | 1710 |
| 138 and 180 | 4140 |