Least Common Multiple (LCM) of 112 and 90
The least common multiple (LCM) of 112 and 90 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 90?
First, calculate the GCD of 112 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 90 = 1 remainder 22 |
| 2 | 90 ÷ 22 = 4 remainder 2 |
| 3 | 22 ÷ 2 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 140 | 420 |
| 156 and 68 | 2652 |
| 105 and 105 | 105 |
| 65 and 195 | 195 |
| 192 and 38 | 3648 |