Least Common Multiple (LCM) of 112 and 73
The least common multiple (LCM) of 112 and 73 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 112 and 73?
First, calculate the GCD of 112 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 73 = 1 remainder 39 |
| 2 | 73 ÷ 39 = 1 remainder 34 |
| 3 | 39 ÷ 34 = 1 remainder 5 |
| 4 | 34 ÷ 5 = 6 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 68 | 1088 |
| 105 and 12 | 420 |
| 186 and 47 | 8742 |
| 118 and 97 | 11446 |
| 131 and 73 | 9563 |