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[Smart Math] Arithmetic Problem 4

Here’s and example of a SMART MATH problem for 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

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

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’.