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Arithmetic Smart Math

[Smart Math] Arithmetic Problem 22

Here’s and example of a SMART MATH problem for ARITHMETIC.

Arithmetic

Problem

Find the LCM of \frac{4}{5}, \frac{3}{4} and \frac{5}{7}.

  1. \frac{5}{12}
  2. 1
  3. 20
  4. 60
  5. \frac{60}{7}

The Usual Method

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First find the LCM of the numerators = 4 x 3 x 5 = 60

HCF of denominators = 1

LCM of fractions =     LCM of numerators

HCF of denominators

=          \frac{60}{1} = 60

(Ans: 4)

Estimated Time to arrive at the answer = 30 seconds.

Using Technique

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Since HCF of any set with a prime number in it is always 1, denominator will be = 1. This eliminates options ‘1’ and ‘5’.

LCM of numerators = product of numerators if they are relatively prime

Hence LCM of the numerators = 4 x 3 x 5 = 60

Hence answer = 60

(Note: The example here is seemingly simple but the important part is the approach in the technique. This approach is universal in its application and so can be applied to other more complex problems also).

(Ans: 4)

Estimated Time to arrive at the answer = 10 seconds.
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