Adam drew two samw size rectangles and divide them into the same number of equal parts. He shaded 1/3 of one rectangle an 1/4 of the other rectangle. What is the west number of parts into which both rectángles could one divided

Question

Daisy Conner

Mathematics

3 July, 00:41

Adam drew two samw size rectangles and divide them into the same number of equal parts. He shaded 1/3 of one rectangle an 1/4 of the other rectangle. What is the west number of parts into which both rectángles could one divided

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Answers (1)

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Jeramiah Mckenzie · Answer 1

12

Step-by-step explanation:

The least common multiple (LCM) of 3 and 4 is their product, 12. Both rectangles were divided into 12 parts.

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The problem is also characterized as finding the least common denominator (LCD) of 1/3 and 1/4. The LCD of 1/3 and 1/4 is the LCM of 3 and 4. There are a couple of ways to find the LCM of two numbers. When those numbers differ by 1, their LCM is their product.

One way is to divide the product by the greatest common factor (GCF). That is ...

LCM (a, b) = a*b/GCF (a, b)

The greatest common factor of two numbers is at most their difference, so when the numbers differ by 1, their GCF is 1. More precisely, their GCF is at most the non-zero remainder when one is divided by the other. If the remainder is non-zero, the GCF is the GCF of that remainder and the smaller of the two numbers. If the remainder is zero, the GCF is the divisor.

Another way to find the GCF is to list the factors (divisors) of each number and find the largest one common to both numbers. When the numbers have many divisors, this process can be shortened somewhat by looking at the list of prime factors. The GCF is the product of the largest of the common prime factors.

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Once you have a list of prime factors of the numbers, you can also find their LCM by forming the product of the largest powers of the unique prime factors. For example, the LCM of 6=2·3 and 8=2³ is 2³·3 = 24.