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- GCD and LCM Calculator

This calculator will find Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of two or more
numbers. **Step-by-step explanation is provided.**

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examples

example 1:ex 1:

What is the Greatest Common Divisor (GCD) of 104 and 64?

example 2:ex 2:

Find the Greatest Common Divisor of 96, 144 and 192.

example 3:ex 3:

Find the Least Common Multiple (LCM) of 8 and 10.

example 4:ex 4:

Find the Least Common Multiple (LCM) of 20, 50 and 65.

**GCD** stands for Greatest Common Divisor. **GCD** is largest number that divides the given numbers. The **GCD** is sometimes called the greatest common factor (**GCF**).

*Find the GCD (GCF) of 45 and 54.*

**Step 1:** Find the divisors of given numbers:

The divisors of 45 are : 1, 3, 5, **9**, 15, 45

The divisors of 54 are : 1, 2, 3, 6, **9**, 18, 27, 54

**Step 2:** Find the greatest number that these two lists share in common. In this example the GCD is 9.

**LCM** stands for Lowest Common Multiple. LCM is the smallest number
that is a multiple of both a and b.

*Find the LCM of 6 and 8.*

The multiples of 6 are : 6, 12, 18, **24**, 30, . . .

The multiples of 8 are : 8, 16, **24**, 32, 40, . . .

So, the Lowest Common Multiple is 24.

Also, we can calculate the LCM using the following formula:

$$ lcm(a,b) = \frac{a \cdot b}{ gcd(a,b)}$$

Now we can find the LCM of 6 and 8 as:

$$ lcm(6,8) = \frac{6 \cdot 8}{ gcd(6,8)} = \frac{48}{2} = 24$$

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