Least Common Multiple (LCM) of 112 and 146
The least common multiple (LCM) of 112 and 146 is 8176.
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 146?
First, calculate the GCD of 112 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 146 = 0 remainder 112 |
| 2 | 146 ÷ 112 = 1 remainder 34 |
| 3 | 112 ÷ 34 = 3 remainder 10 |
| 4 | 34 ÷ 10 = 3 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 110 | 990 |
| 27 and 175 | 4725 |
| 123 and 178 | 21894 |
| 84 and 79 | 6636 |
| 109 and 151 | 16459 |