Least Common Multiple (LCM) of 31 and 51
The least common multiple (LCM) of 31 and 51 is 1581.
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 51?
First, calculate the GCD of 31 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 51 = 0 remainder 31 |
| 2 | 51 ÷ 31 = 1 remainder 20 |
| 3 | 31 ÷ 20 = 1 remainder 11 |
| 4 | 20 ÷ 11 = 1 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 42 | 1218 |
| 121 and 116 | 14036 |
| 164 and 18 | 1476 |
| 118 and 194 | 11446 |
| 183 and 172 | 31476 |