Least Common Multiple (LCM) of 180 and 112
The least common multiple (LCM) of 180 and 112 is 5040.
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 180 and 112?
First, calculate the GCD of 180 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 112 = 1 remainder 68 |
| 2 | 112 ÷ 68 = 1 remainder 44 |
| 3 | 68 ÷ 44 = 1 remainder 24 |
| 4 | 44 ÷ 24 = 1 remainder 20 |
| 5 | 24 ÷ 20 = 1 remainder 4 |
| 6 | 20 ÷ 4 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 128 | 5760 |
| 113 and 116 | 13108 |
| 96 and 71 | 6816 |
| 22 and 184 | 2024 |
| 193 and 34 | 6562 |