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 |
|---|---|
| 162 and 20 | 1620 |
| 140 and 175 | 700 |
| 153 and 35 | 5355 |
| 177 and 87 | 5133 |
| 192 and 200 | 4800 |