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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.

GCD and LCM Calculator
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 Greatest Common Divisor (GCD) Least Common Multiple (LCM)
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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).

### GCD Example

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.

### LCM Example

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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