Least Common Multiple (LCM) of 32 and 185
The least common multiple (LCM) of 32 and 185 is 5920.
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 185?
First, calculate the GCD of 32 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 185 = 0 remainder 32 |
| 2 | 185 ÷ 32 = 5 remainder 25 |
| 3 | 32 ÷ 25 = 1 remainder 7 |
| 4 | 25 ÷ 7 = 3 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 37 | 5106 |
| 87 and 67 | 5829 |
| 81 and 20 | 1620 |
| 94 and 148 | 6956 |
| 25 and 104 | 2600 |