Least Common Multiple (LCM) of 73 and 112
The least common multiple (LCM) of 73 and 112 is 8176.
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 112?
First, calculate the GCD of 73 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 112 = 0 remainder 73 |
| 2 | 112 ÷ 73 = 1 remainder 39 |
| 3 | 73 ÷ 39 = 1 remainder 34 |
| 4 | 39 ÷ 34 = 1 remainder 5 |
| 5 | 34 ÷ 5 = 6 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 35 | 1785 |
| 156 and 58 | 4524 |
| 174 and 60 | 1740 |
| 193 and 92 | 17756 |
| 60 and 80 | 240 |