Least Common Multiple (LCM) of 112 and 180
The least common multiple (LCM) of 112 and 180 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 112 and 180?
First, calculate the GCD of 112 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 180 = 0 remainder 112 |
| 2 | 180 ÷ 112 = 1 remainder 68 |
| 3 | 112 ÷ 68 = 1 remainder 44 |
| 4 | 68 ÷ 44 = 1 remainder 24 |
| 5 | 44 ÷ 24 = 1 remainder 20 |
| 6 | 24 ÷ 20 = 1 remainder 4 |
| 7 | 20 ÷ 4 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 178 | 7120 |
| 98 and 184 | 9016 |
| 55 and 92 | 5060 |
| 67 and 183 | 12261 |
| 19 and 123 | 2337 |