Least Common Multiple (LCM) of 112 and 181
The least common multiple (LCM) of 112 and 181 is 20272.
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 181?
First, calculate the GCD of 112 and 181 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 181 = 0 remainder 112 |
| 2 | 181 ÷ 112 = 1 remainder 69 |
| 3 | 112 ÷ 69 = 1 remainder 43 |
| 4 | 69 ÷ 43 = 1 remainder 26 |
| 5 | 43 ÷ 26 = 1 remainder 17 |
| 6 | 26 ÷ 17 = 1 remainder 9 |
| 7 | 17 ÷ 9 = 1 remainder 8 |
| 8 | 9 ÷ 8 = 1 remainder 1 |
| 9 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 20 | 220 |
| 52 and 189 | 9828 |
| 189 and 38 | 7182 |
| 182 and 44 | 4004 |
| 63 and 131 | 8253 |