Least Common Multiple (LCM) of 114 and 88
The least common multiple (LCM) of 114 and 88 is 5016.
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 114 and 88?
First, calculate the GCD of 114 and 88 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 88 = 1 remainder 26 |
| 2 | 88 ÷ 26 = 3 remainder 10 |
| 3 | 26 ÷ 10 = 2 remainder 6 |
| 4 | 10 ÷ 6 = 1 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 163 | 27384 |
| 174 and 144 | 4176 |
| 174 and 78 | 2262 |
| 113 and 55 | 6215 |
| 199 and 82 | 16318 |