Least Common Multiple (LCM) of 112 and 40
The least common multiple (LCM) of 112 and 40 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 40?
First, calculate the GCD of 112 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 40 = 2 remainder 32 |
| 2 | 40 ÷ 32 = 1 remainder 8 |
| 3 | 32 ÷ 8 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 36 | 900 |
| 157 and 53 | 8321 |
| 84 and 166 | 6972 |
| 198 and 38 | 3762 |
| 67 and 191 | 12797 |