# Aptitude - Problems on H.C.F and L.C.M - Discussion

### Discussion :: Problems on H.C.F and L.C.M - General Questions (Q.No.29)

29.

 The H.C.F. of 9 , 12 , 18 and 21 is: 10 25 35 40

[A].
 3 5
[B].
 252 5
[C].
 3 1400
[D].
 63 700

Answer: Option C

Explanation:

 Required H.C.F. = H.C.F. of 9, 12, 18, 21 = 3 L.C.M. of 10, 25, 35, 40 1400

 Bhushan said: (Dec 25, 2010) Is this the correct answer?

 Aparna said: (Dec 27, 2010) Ya, its exactly the right answer.

 Vivek Chandra Mishra said: (Apr 24, 2011) Here hcf of 9=3*3,12=3*2*2,18=3*3*2,21=3*7 HCF=3 LCM of 10=2*5,25=5*5,35=3*7,40=2*2*2*5 LCM=1400 Required hcf = hcf/lcm =3/1400

 Manasa said: (Jul 13, 2011) How we get 1400 in the lcm part? Please can any one explain ?

 Keta said: (Jul 22, 2011) Can you please explain in depth. ?

 Zafar Khan said: (Oct 16, 2011) H.C.F= H.C.F of Numerators/L.C.M of Denominators L.C.M= L.C.M of Numerators/H.C.F of Denominators

 Vani Varma said: (Feb 8, 2012) @manasa 5 10 25 35 40 2 2 5 7 8 1 5 7 4 lcm = 5*2*1*5*7*4 = 1400

 Amrit Kaur said: (Oct 5, 2012) Any other method to find H.C.F ?

 Rajesh said: (Jun 29, 2013) Can anyone explain, how this method give H.C.F?

 Sirisha said: (Jul 7, 2013) 9/10, 12/25, 18/35, 21/40 is the given problem. H.C.F of numerators, 9 = 3*3. 12 = 3*2*2. 18 = 2*3*3. 21 = 7*3. Common least factors of these numbers is 3(h.c.f). L.C.M of denominators, 10 = 2*5. 25 = 5*5. 35 = 7*5. 40 = 5*2*2*2. Highest factors of all these numbers is 1400(2*2*2*5*5*7). So final answer is 3/1400.

 Electronics said: (Oct 7, 2013) The concept behind hcf/lcm is that suppose we take 9/10 now there should be a fraction a/b that exactly divides it (9/10) / (a/b) = (9*b) / (10*a) now you take a as hcf of all numbers (numerators only) that will exactly divide 9. Now for b if you take hcf of denominators it will exactly divide 10 but now there will be a number in denominator of our expression giving us fraction but if we rather take lcm then 10 will go in integral number to divide b and we will get integer.

 Rauf Lala said: (Apr 21, 2014) What is the need for so much of calculations? Since we know that HCF of any fraction is computed with the following formula = HCF of Numerators/LCM of denominators. Now see the Options: Numerators has to be less than the given numbers (9, 12, 18, 21) since, it is HCF. This rules out Options B and D. We are left with options A and C. Now denominator is the LCM which shall be more than the given number i.e. 10, 25, 35, 40. Therefore Options C is the correct answer.

 Anil said: (Sep 16, 2014) Can you please explain shortcut?

 Mozzima said: (Jul 6, 2015) Why we have taken LCM of denominator?

 Lalu said: (Mar 12, 2016) Thats long process, tell me short cut method.

 Dillip said: (Jun 18, 2016) Actually, the answer is showing 3/2800. That's why getting confused. I also got the result 3/1400.

 Sanjuu S said: (Jun 29, 2016) Simply Here HCF of 9 =3 * 3, 12 = 3 * 2 * 2, 18 = 3 * 3 * 2, and 21 = 3 * 7. HCF = 3. LCM of 10 =2 * 5, 25 = 5* 5, 35 = 3 * 7, 40 = 2* 2 * 2 * 5. LCM = 1400. Required HCF = HCF/LCM. = 3/1400.

 Amit said: (Sep 20, 2016) Answer Should be 3/2800. Because, H.C.F of 9, 12, 18, 21 is 3. L.C.M of 10, 25, 35, 40 is 2800. So, the answer is 3/2800.

 Amir said: (Jan 11, 2017) If we take LCM collectively, the HCF is 2 and 3, if one by one it's 3. How can we recognise that the HCF should be taken separately?

 Sanidhya said: (Jul 21, 2017) Why isn't the answer 3/5 as 3/5 divides all numbers and it is also higher than 3/1400?

 Lateef said: (Aug 31, 2017) Agree @Sanidhya. Can anyone explain us?

 Arunava said: (Sep 23, 2017) Agree @Sanidhya. Please explain.

 Gopal said: (Mar 7, 2018) For the same question instead of hcf if LCM was asked what will be the answer? Please solve it.

 Rahul Dhamala said: (Jun 22, 2018) I am not getting the answer. Please explain.

 Sruthi said: (Sep 2, 2018) Hi. Isn't the answer 3/5? How did it become 3/1400? The number obtained by dividing 3 by 5 is greater than the number obtained by dividing 3 by 1400. Besides what is the credibility of the formula to find the hcf of a fraction? And also 3/5 can be used to divide all the four fractions in the question. If the question is to find the HCF of fractions then why can't the HCF we obtain, when used to divide the fractions in the question give us fractions rather than integers?

 Saidaiah said: (Sep 27, 2018) The Lcm is 3/2800.

 Rohit said: (Mar 31, 2020) I got lcm 2800 but here it is 1400. Please anyone explain this in detail.

 Ramniwas Dudhwal said: (May 29, 2020) 2/10, 25, 35, 40. 2/5, 25, 35, 20, 2/5, 25, 35, 10, 5/5, 25, 35, 5, 5/1, 5, 7, 1, 7/1, 1, 1, 1. LCM = 2 * 2 * 2 * 5 * 5 * 7 = 1400.

 R K Vidhyaa said: (May 17, 2021) I too agree, the answer is 3/5.

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