Least Common Multiple (LCM) of 31 and 57
The least common multiple (LCM) of 31 and 57 is 1767.
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 57?
First, calculate the GCD of 31 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 57 = 0 remainder 31 |
| 2 | 57 ÷ 31 = 1 remainder 26 |
| 3 | 31 ÷ 26 = 1 remainder 5 |
| 4 | 26 ÷ 5 = 5 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 49 | 3577 |
| 100 and 129 | 12900 |
| 144 and 45 | 720 |
| 14 and 123 | 1722 |
| 142 and 13 | 1846 |