Least Common Multiple (LCM) of 176 and 114
The least common multiple (LCM) of 176 and 114 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 176 and 114?
First, calculate the GCD of 176 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 114 = 1 remainder 62 |
| 2 | 114 ÷ 62 = 1 remainder 52 |
| 3 | 62 ÷ 52 = 1 remainder 10 |
| 4 | 52 ÷ 10 = 5 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 91 | 13832 |
| 89 and 109 | 9701 |
| 175 and 36 | 6300 |
| 197 and 113 | 22261 |
| 50 and 144 | 3600 |