Least Common Multiple (LCM) of 32 and 91
The least common multiple (LCM) of 32 and 91 is 2912.
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 91?
First, calculate the GCD of 32 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 91 = 0 remainder 32 |
| 2 | 91 ÷ 32 = 2 remainder 27 |
| 3 | 32 ÷ 27 = 1 remainder 5 |
| 4 | 27 ÷ 5 = 5 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 155 | 1395 |
| 105 and 78 | 2730 |
| 189 and 35 | 945 |
| 138 and 41 | 5658 |
| 95 and 175 | 3325 |