Least Common Multiple (LCM) of 32 and 96
The least common multiple (LCM) of 32 and 96 is 96.
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 96?
First, calculate the GCD of 32 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 96 = 0 remainder 32 |
| 2 | 96 ÷ 32 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 105 | 840 |
| 38 and 97 | 3686 |
| 17 and 99 | 1683 |
| 137 and 105 | 14385 |
| 167 and 62 | 10354 |