Least Common Multiple (LCM) of 31 and 47
The least common multiple (LCM) of 31 and 47 is 1457.
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 47?
First, calculate the GCD of 31 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 47 = 0 remainder 31 |
| 2 | 47 ÷ 31 = 1 remainder 16 |
| 3 | 31 ÷ 16 = 1 remainder 15 |
| 4 | 16 ÷ 15 = 1 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 126 | 2898 |
| 53 and 196 | 10388 |
| 103 and 170 | 17510 |
| 169 and 143 | 1859 |
| 137 and 158 | 21646 |