Least Common Multiple (LCM) of 32 and 84
The least common multiple (LCM) of 32 and 84 is 672.
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 84?
First, calculate the GCD of 32 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 84 = 0 remainder 32 |
| 2 | 84 ÷ 32 = 2 remainder 20 |
| 3 | 32 ÷ 20 = 1 remainder 12 |
| 4 | 20 ÷ 12 = 1 remainder 8 |
| 5 | 12 ÷ 8 = 1 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 18 | 882 |
| 163 and 116 | 18908 |
| 140 and 69 | 9660 |
| 96 and 193 | 18528 |
| 17 and 158 | 2686 |