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 |
|---|---|
| 59 and 98 | 5782 |
| 128 and 198 | 12672 |
| 193 and 60 | 11580 |
| 200 and 165 | 6600 |
| 153 and 197 | 30141 |