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# [Smart Math] Arithmetic Problem 10

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

### Problem

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

1. 734
2. 735
3. 524
4. 510
5. 786

### The Usual Method

We know that HCF x LCM = product of two numbers

Let HCF = x

$\therefore$ One number = 5x and another number = 7x

$\therefore$ LCM = 35x

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

$\therefore$ x = 21 = HCF.

$\therefore$ LCM = 35 x 21 = 735

(Ans: 2)

Estimated Time to arrive at the answer = 45 seconds.