Least Common Multiple (LCM) of 80 and 112
The least common multiple (LCM) of 80 and 112 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 80 and 112?
First, calculate the GCD of 80 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 112 = 0 remainder 80 |
| 2 | 112 ÷ 80 = 1 remainder 32 |
| 3 | 80 ÷ 32 = 2 remainder 16 |
| 4 | 32 ÷ 16 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 104 | 8840 |
| 72 and 45 | 360 |
| 50 and 187 | 9350 |
| 99 and 133 | 13167 |
| 99 and 58 | 5742 |