Least Common Multiple (LCM) of 116 and 45
The least common multiple (LCM) of 116 and 45 is 5220.
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 116 and 45?
First, calculate the GCD of 116 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 45 = 2 remainder 26 |
| 2 | 45 ÷ 26 = 1 remainder 19 |
| 3 | 26 ÷ 19 = 1 remainder 7 |
| 4 | 19 ÷ 7 = 2 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 188 | 4324 |
| 21 and 128 | 2688 |
| 110 and 43 | 4730 |
| 71 and 77 | 5467 |
| 166 and 70 | 5810 |