Least Common Multiple (LCM) of 112 and 162
The least common multiple (LCM) of 112 and 162 is 9072.
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 162?
First, calculate the GCD of 112 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 162 = 0 remainder 112 |
| 2 | 162 ÷ 112 = 1 remainder 50 |
| 3 | 112 ÷ 50 = 2 remainder 12 |
| 4 | 50 ÷ 12 = 4 remainder 2 |
| 5 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 71 | 7455 |
| 137 and 75 | 10275 |
| 57 and 130 | 7410 |
| 105 and 60 | 420 |
| 43 and 155 | 6665 |