Least Common Multiple (LCM) of 113 and 146
The least common multiple (LCM) of 113 and 146 is 16498.
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 113 and 146?
First, calculate the GCD of 113 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 146 = 0 remainder 113 |
| 2 | 146 ÷ 113 = 1 remainder 33 |
| 3 | 113 ÷ 33 = 3 remainder 14 |
| 4 | 33 ÷ 14 = 2 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 49 | 7595 |
| 132 and 90 | 1980 |
| 89 and 180 | 16020 |
| 137 and 118 | 16166 |
| 175 and 177 | 30975 |