Least Common Multiple (LCM) of 32 and 46
The least common multiple (LCM) of 32 and 46 is 736.
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 46?
First, calculate the GCD of 32 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 46 = 0 remainder 32 |
| 2 | 46 ÷ 32 = 1 remainder 14 |
| 3 | 32 ÷ 14 = 2 remainder 4 |
| 4 | 14 ÷ 4 = 3 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 54 | 108 |
| 51 and 178 | 9078 |
| 104 and 21 | 2184 |
| 129 and 178 | 22962 |
| 45 and 176 | 7920 |