Least Common Multiple (LCM) of 112 and 145
The least common multiple (LCM) of 112 and 145 is 16240.
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 145?
First, calculate the GCD of 112 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 145 = 0 remainder 112 |
| 2 | 145 ÷ 112 = 1 remainder 33 |
| 3 | 112 ÷ 33 = 3 remainder 13 |
| 4 | 33 ÷ 13 = 2 remainder 7 |
| 5 | 13 ÷ 7 = 1 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 13 | 2236 |
| 167 and 29 | 4843 |
| 47 and 49 | 2303 |
| 130 and 144 | 9360 |
| 120 and 114 | 2280 |