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Arithmetic Smart Math

[Smart Math] Arithmetic Problem 4

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

Arithmetic

Problem

Find the HCF and LCM of 6a^{2}b^{3}, 9a^{5}b and 12a^{2}bc^{2}

  1. 3a^{2}b^{{}}; 18a^{4}b^{5}c^{{}}
  2. 9a^{2}b^{2}; 36a^{5}b^{3}c^{2}
  3. 6ab^{2}; 18a^{4}b^{4}c^{{}}
  4. 3a^{2}b; 36a^{5}b^{3}c^{2}
  5. None of these

The Usual Method

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To find HCF, looking at the common terms amongst the expressions, we get:

HCF = 3a^{2}b^{{}}

To get the LCM, we multiply the HCF 3a^{2}b^{{}} with all the remaining terms of the expressions and we will get LCM = 36a^{5}b^{3}c^{2}

(Ans: 4)

Estimated Time to arrive at the answer = 45 seconds

Using Technique

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Visually you can find the HCF as 3a^{2}b^{{}} as ‘3’, ‘a^{2}’ and ‘b’ are the only terms common in all the three expressions. This eliminates options ‘2’ and ‘3’.

Also note that the LCM must have ‘c^{2}’, as it is the only term appearing in the third expression and not in the other two expressions. Hence, answer is option ‘4’.

(Ans: 4)

Estimated Time to arrive at the answer = 5 seconds
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