Least Common Multiple (LCM) of 32 and 178
The least common multiple (LCM) of 32 and 178 is 2848.
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 32 and 178?
First, calculate the GCD of 32 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 178 = 0 remainder 32 |
| 2 | 178 ÷ 32 = 5 remainder 18 |
| 3 | 32 ÷ 18 = 1 remainder 14 |
| 4 | 18 ÷ 14 = 1 remainder 4 |
| 5 | 14 ÷ 4 = 3 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 132 | 396 |
| 116 and 153 | 17748 |
| 48 and 75 | 1200 |
| 68 and 124 | 2108 |
| 48 and 142 | 3408 |