Least Common Multiple (LCM) of 31 and 37
The least common multiple (LCM) of 31 and 37 is 1147.
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 37?
First, calculate the GCD of 31 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 37 = 0 remainder 31 |
| 2 | 37 ÷ 31 = 1 remainder 6 |
| 3 | 31 ÷ 6 = 5 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 14 | 658 |
| 73 and 156 | 11388 |
| 159 and 50 | 7950 |
| 153 and 153 | 153 |
| 30 and 175 | 1050 |