Least Common Multiple (LCM) of 132 and 178
The least common multiple (LCM) of 132 and 178 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 132 and 178?
First, calculate the GCD of 132 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 178 = 0 remainder 132 |
| 2 | 178 ÷ 132 = 1 remainder 46 |
| 3 | 132 ÷ 46 = 2 remainder 40 |
| 4 | 46 ÷ 40 = 1 remainder 6 |
| 5 | 40 ÷ 6 = 6 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 194 | 1358 |
| 100 and 130 | 1300 |
| 21 and 118 | 2478 |
| 60 and 87 | 1740 |
| 82 and 170 | 6970 |