Least Common Multiple (LCM) of 112 and 80
The least common multiple (LCM) of 112 and 80 is 560.
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 80?
First, calculate the GCD of 112 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 80 = 1 remainder 32 |
| 2 | 80 ÷ 32 = 2 remainder 16 |
| 3 | 32 ÷ 16 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 111 | 1887 |
| 31 and 149 | 4619 |
| 129 and 149 | 19221 |
| 40 and 108 | 1080 |
| 103 and 104 | 10712 |