# CAT Practice : Number System - HCF, LCM

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HCF of fractions

## Sum of the digits

Q.12: 4 logs of woods of lengths 5 1/4 m, 1 13/15 m, 3 1/2 m and 4 9/10 m are cut into small pieces, all of which have equal length. Each piece of wood is as lengthy as possible. Each cut piece is given to a set of 2 carpenters to work on something. How many carpenters are there in all to work?
1. 148
2. 210
3. 332
4. 266

Choice D. 266

## Detailed Solution

HCF (5 $\frac{1}{4}$ , 1 $\frac{13}{15}$ , 3 $\frac{1}{2}$ , 4 $\frac{9}{10}$)

= HCF ($\frac{21}{4}$ , $\frac{28}{15}$ , $\frac{7}{2}$ , $\frac{49}{10}$)

= $\frac{HCF(21, 28, 7, 49)}{LCM(4, 15, 2, 10)}$

= $\frac{7}{60}$

Hence, total number of pieces
= $\frac{21}{4}$ * $\frac{60}{7}$ + $\frac{28}{15}$ * $\frac{60}{7}$ + $\frac{7}{2}$ * $\frac{60}{7}$ + $\frac{49}{10}$ * $\frac{60}{7}$

= 45 + 16 + 30 + 42
= 133

Total number of carpenters required = 133 * 2 = 266

Choice D

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## More questions from Number Theory - HCF, LCM

Number Theory is one of the most heavily tested topics. Within this, one should get the basics on factors, multiples, HCF, LCM very clear before moving on to the tougher sets.