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

**Problem**

**Problem**

HCF of two numbers is 1/5^{th} of a number and 1/7^{th} of the other number. The difference between the numbers is 42. What is the LCM?

- 734
- 735
- 524
- 510
- 786

**The Usual Method**

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We know that HCF x LCM = product of two numbers

Let HCF = *x*

One number = 5*x* and another number = 7*x*

LCM = 35*x*

Also, difference between numbers = 7*x* – 5*x* = 2*x* = 42 (given)

*x* = 21 = HCF.

LCM = 35 x 21 = 735

** **

**(Ans: 2)**

*Estimated Time to arrive at the answer = 45 seconds.*

**Using Technique**

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Looking at the information in the problem, it is evident that the LCM is a multiple of 7 and 5. The only option that is a multiple of 7 and 5 amongst the options is option ‘2’.

**(Ans: 2)**

*Estimated Time to arrive at the answer = 5 seconds.*

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