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 |
|---|---|
| 65 and 90 | 1170 |
| 92 and 174 | 8004 |
| 149 and 116 | 17284 |
| 142 and 41 | 5822 |
| 57 and 39 | 741 |