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 |
|---|---|
| 144 and 116 | 4176 |
| 165 and 110 | 330 |
| 22 and 49 | 1078 |
| 148 and 133 | 19684 |
| 99 and 102 | 3366 |