Least Common Multiple (LCM) of 46 and 113
The least common multiple (LCM) of 46 and 113 is 5198.
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 46 and 113?
First, calculate the GCD of 46 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 113 = 0 remainder 46 |
| 2 | 113 ÷ 46 = 2 remainder 21 |
| 3 | 46 ÷ 21 = 2 remainder 4 |
| 4 | 21 ÷ 4 = 5 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 193 | 17177 |
| 143 and 26 | 286 |
| 23 and 98 | 2254 |
| 165 and 130 | 4290 |
| 64 and 182 | 5824 |