Least Common Multiple (LCM) of 73 and 31
The least common multiple (LCM) of 73 and 31 is 2263.
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 73 and 31?
First, calculate the GCD of 73 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 31 = 2 remainder 11 |
| 2 | 31 ÷ 11 = 2 remainder 9 |
| 3 | 11 ÷ 9 = 1 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 123 | 22755 |
| 80 and 44 | 880 |
| 180 and 17 | 3060 |
| 135 and 147 | 6615 |
| 162 and 16 | 1296 |