Ratio of two numbers and LCM is given

Discussion :: Problems on H.C.F and L.C.M - General Questions (Q.No.18)

18.

The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:

[A].	12
[B].	16
[C].	24
[D].	48

Answer: Option D

Explanation:

Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.

So, the numbers 12 and 16.

L.C.M. of 12 and 16 = 48.

Jayshree said: (Apr 14, 2011)
Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4. i understand this step but i dont understand this step he numbers 12 and 16. please explain.

Suyash said: (May 19, 2011)
Hey jayshree Given hcf = 4 =3x=3x4=12 4x=4x4=16 multiply 3 with 16 and 4 with 12 answer is 48 got it!

Nisha said: (Jun 12, 2011)

Please tell me why use h.c.f value instead of x hcf * lcm= pro. of no 4*lcm=3x*4x lcm=3x*4x/4

reply according to this

Reuben said: (Jul 25, 2011)
hcf of any two numbers is a factor of those two numbers .. means example if u take hcf of 12 and 18 .. its 6 .. it means 6 is a factor of 12 and 18. 62=12 63=18 now if i say there are two numbers in ratio 2:3 whose hcf is 6 how will u write the two numbers ?? solve my question and u will understand it ans: hcf2 is one number hcf3 is the other

Fakir Chand Bhatt said: (Dec 29, 2011)
L.C.M. OF 3 : 4 IS ............. 12 AND THE H.C.F IS GIVEN 4 IN THE QUESTION NOW , REQUIRED NUMBER IS [12*4] = 48 ANSWER IS THE WAY IS RIGHT OR NOT.........

Karan Kashyap said: (Feb 10, 2012)
Easy and time saving trick is. 3:4= 34 = 12. 12hcf=>>>> 12*4=48 answer.

Kinjal said: (May 27, 2013)
I understand that assume numbers are 3x & 4x so hcf is x. But now how x is equals to 4?

Nik said: (Aug 5, 2013)
@Kinjal. Find out the common multiple of 4&3 you will get the answer.

Rosy said: (Aug 21, 2013)
As nisha said, ab = lcmhcf 34 = 4lcm We get value lcm = 3. Why can't we do in this method?

Mohanlal Vishwanathan Nair said: (Apr 17, 2014)

3:4 = 3*4 = 12.

12*HCF = 12*4 = 48.

Pritam said: (May 3, 2014)
Initially let the two numbers be 3x and 4x and there given h.c.f is 4. So that means 3x and 4x are the product of a number and a variable which is = to the product of h.c.f and l.c.m as we know.now h.c.f given here is 4. So put 4 instead of x and get the numbers i.e 12 and 16. Find the l.c.m of these two numbers i.e 48.

Mintu Bhusan Singha said: (Nov 18, 2014)
Excellent information.

Arjun Singh said: (Feb 12, 2015)
3x = 3 (4 H.C.F) = 12. 4x = 4 (4 H.C.F) = 16. LCM of 12 & 16. 12 = 223. 16 = 2222. Now we have 223222*2 = 192. HCF = 4/LCM 192. 4/192 = 48 answer. Got it or not.

Neha said: (Feb 21, 2015)
You can't get 48 by 4/192 you can get 48 by 192/4.

Sukumar Satyen said: (Apr 9, 2015)
Let the numbers be 3x and 4x. We know that 3x4x = HCFLCM. => 12x^2 = 4LCM. => LCM = 3x^2.....equation (1). L.C.M. of 3x, 4x = 12x.....equation (2). Now, equation(1) = equation(2). => 3x^2 = 12x. => x = 4. => L.C.M = 12x = 124 = 48. Thanks.

Homay said: (Apr 30, 2015)
HCF = 4 (given). Say m = 4. LCM = Product of two numbers/HCF. = 3m4m/m. = 1216/4. = 48.

Kuldeep said: (Aug 25, 2015)
The product of two numbers is 724 and HCF is 4 then find the LCM?

Anupam Kumar Yadav said: (Sep 2, 2015)

The sum of two number is 420 and one of them is 260. Find the product of the two numbers.

Find the greatest number of 4 digits which is divisible by 35.

Jc N said: (Apr 17, 2016)

Since the ratio is given and the HCF as well, we now know that there will not be any other factor other than the ratio * HCF for both the numbers. Because if there are any more factors then the HCF will increase by that number. So the two numbers have to be 3*HCF and 4*HCF.

Eg: Suppose we say that HCF is not the only other factor than the number could be 3*HCF*x and 4*HCF*Y, now for the ratio to be 3:4, x = why. But x=why then we have another common factor for the two numbers and the HCF would then be HCF*x which is not true as per the given question. Thus, there should be no other common factor. Thus, we can say whenever the ratio and HCF are given the numbers are always ratio * HCF.

Ashif said: (May 26, 2016)
The product of HCF 18 and LCM 16 is? Can anyone help to get the answer?

Dipali Patkar said: (Aug 9, 2016)
@Ashif. 18 * 16 = 288.

Onkar Rana said: (Dec 25, 2016)
Why they put x = 4? Explain me.

Pranathi said: (Feb 25, 2017)
4 * lcm=3x * 4x. 4 * lcm=3 * 4 * 4 * 4, Lcm = 12 * 16 ÷ 4. = 48 -> Is this correct?

Kushal said: (May 24, 2017)
Here given two ratios are 3:4 and given HCF is 4 so that's the highest common factor so one can think that could be multiple of 3:4. So just multiplied with 34 and 44 so two numbers we get are 12 and 16 take out LCM by 12->223 and of 16->2222-> 2232*2->48.

Rupesh said: (Jun 15, 2018)

Hcf = product/lcm. = 3*4+4*4/4.

= 48.

Arul said: (Jul 14, 2018)
How x=3 why not 4? LCMHCF=product. X4=3x*4x. X=3.

Rahul said: (Oct 23, 2018)
3x ,4x be the two numbers and the given Question HCF is given so take HCF of (3, 4) = 1x. So x = 4. 34=12, 44=16, LCM = 48.

Hema said: (Apr 15, 2019)
4x*3x = 12x. 12x= 4(hcf), So x=3. How 4?

Tulasi said: (May 30, 2020)
How come x as 4? Please explain to me.

Manish Kumar said: (Feb 14, 2021)
Let numbers be 3x and 4x. LCM 12x. Also 3x 4x=LCMHCF. 3x*4x=12x. X=4. Numbers are 12, 16. LCM =12x = 48 is the answer.