Least Common Multiple (LCM) of 43 and 116
The least common multiple (LCM) of 43 and 116 is 4988.
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 43 and 116?
First, calculate the GCD of 43 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 116 = 0 remainder 43 |
| 2 | 116 ÷ 43 = 2 remainder 30 |
| 3 | 43 ÷ 30 = 1 remainder 13 |
| 4 | 30 ÷ 13 = 2 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 52 | 9828 |
| 62 and 157 | 9734 |
| 89 and 115 | 10235 |
| 90 and 125 | 2250 |
| 100 and 191 | 19100 |