Least Common Multiple (LCM) of 114 and 176
The least common multiple (LCM) of 114 and 176 is 10032.
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 176?
First, calculate the GCD of 114 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 176 = 0 remainder 114 |
| 2 | 176 ÷ 114 = 1 remainder 62 |
| 3 | 114 ÷ 62 = 1 remainder 52 |
| 4 | 62 ÷ 52 = 1 remainder 10 |
| 5 | 52 ÷ 10 = 5 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 67 | 670 |
| 145 and 27 | 3915 |
| 149 and 187 | 27863 |
| 74 and 199 | 14726 |
| 67 and 103 | 6901 |