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# [Smart Math] Arithmetic Problem 22

Here’s and example of a SMART MATH problem for 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

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

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