Least Common Multiple (LCM) of 178 and 132
The least common multiple (LCM) of 178 and 132 is 11748.
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 178 and 132?
First, calculate the GCD of 178 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 132 = 1 remainder 46 |
| 2 | 132 ÷ 46 = 2 remainder 40 |
| 3 | 46 ÷ 40 = 1 remainder 6 |
| 4 | 40 ÷ 6 = 6 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 46 | 8142 |
| 43 and 198 | 8514 |
| 197 and 84 | 16548 |
| 191 and 192 | 36672 |
| 118 and 153 | 18054 |