Least Common Multiple (LCM) of 31 and 75
The least common multiple (LCM) of 31 and 75 is 2325.
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 75?
First, calculate the GCD of 31 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 75 = 0 remainder 31 |
| 2 | 75 ÷ 31 = 2 remainder 13 |
| 3 | 31 ÷ 13 = 2 remainder 5 |
| 4 | 13 ÷ 5 = 2 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 144 | 6192 |
| 82 and 168 | 6888 |
| 27 and 157 | 4239 |
| 171 and 79 | 13509 |
| 20 and 36 | 180 |