The least number which when divided by 12, 15, 20 and 54 leaves remainder 8

Discussion :: Problems on H.C.F and L.C.M - General Questions (Q.No.25)

25.

The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:

[A].	504
[B].	536
[C].	544
[D].	548

Answer: Option D

Explanation:

Required number = (L.C.M. of 12, 15, 20, 54) + 8

= 540 + 8

= 548.

Saritha said: (Dec 16, 2010)
wat is the lcm of 12,15,20 and 54?

Saranya said: (Dec 23, 2010)
lcm=540

Jas said: (Feb 23, 2011)
How? Anybody can explain ?

Prannav said: (May 10, 2011)
Can anyone please show me the procedure to calculate the lcm as I think I am making some mistake.

Suresh said: (Jul 19, 2011)
First divide entire given series with 2 then you have the remainders 6, 15, 10, 27. Now divide these series with 3 then you get reminders 2, 5, 10, 9. Now divide before series with 5 then you will get series 2, 1, 2, 9. Now divide before series with 2 then you will get series 1, 1, 1, 9. Now multliply all the divisors that used in it i.e 23529 = 540.

Gufran said: (Sep 29, 2011)
L.C.M 2 \| 12,15,20,54 2 \| 6 ,15,10,27 3 \| 3 ,15,5 ,27 5 \| 1 ,5 ,5 ,9 1 ,1 ,1 ,9 NOW,22359=540 Required number = (L.C.M. of 12, 15, 20, 54) + 8 = 540 + 8 = 548.

Subhani said: (Nov 17, 2011)
Please anyone tell me what is the least natural number which when divided by 2, 3, 4, 5 or 6 leaves a remainder 1.

Umesh Gupta said: (Feb 11, 2012)
L.C.M 2 \| 2,3,4,5,6 2 \| 1,3,2,5,3, 3 \| 1,3,1,5,3 \| 1,1,1,5,1 NOW,223*5=60 Required number = (L.C.M. of 2, 3, 4, 5 and 6) + 1 = 60 + 1 = 61

Disha said: (Sep 16, 2012)
After calculating the lcm why 8 is added?

Sreera said: (Feb 18, 2013)
Question is what is the number. LCM OF 12, 15, 20 and 54 = 540. Reminder = 8. Exactly The Number is 540 + 8.

Jalpan said: (Mar 10, 2014)
Can any one tell me. Why + ? Why - not ? Because I have seen some examples where, if HCF then taking remainder plus with dividend and if LCM then taking remainder substracted from the dividend. Explain please.

Ayesha said: (Oct 25, 2014)
Yes why it is not like 540k+8?

PKP said: (Jun 3, 2015)
Just divide all the answer options by 20 (because its easy) only option D leaves the remainder 8.

Sushma Sharma said: (Jun 10, 2015)
Can two no. have 25 as their HCF answer 2034 as their LCM? Give reason in support of your answer?

Abdul said: (Jul 22, 2015)
Please explain the sum to me.

Shakti said: (Aug 4, 2015)
Yes why it is not 540k+8?

V!cky said: (Sep 5, 2015)
2\|12 15 20 54. 2\|06 15 10 27. 3\|03 15 05 27. 5\|01 05 05 09. 9\|01 01 01 09. \|01 01 01 01. Best to find LCM solve till all value get 1. You will always get perfect answer without confusion. 22359 = 540.

V!cky said: (Sep 5, 2015)
Just add remainder with it 540+8 = 548.

Vamsi said: (Oct 11, 2015)
Some problem sub to remainder why please explain to me?

Anon said: (Oct 25, 2015)
Shouldn't the answer be 8 here?

Kinjal said: (Feb 18, 2016)
Yes @Jalpan even I am confused as to when you need to subtract and when you need to add the remainder. Can anyone explain?

Unknown said: (Jul 4, 2016)
Please tell me how to find the HCF of 15, 12, 20, 54.

Sharang Rane said: (Aug 1, 2016)
Dividend = Divisor * Quotient + Remainder. That's why +8.

Balaram said: (Jun 19, 2017)
LCM of 12, 15, 20, 24 is 540. Required no is 548. 548 is divided by 12, 15, 20, 24 respectively. The remainder is 8. That is the reason add 8.

Saurabha said: (Oct 24, 2017)

@unknown. Given nor.s in increasing order:12,15,20,54 At the beginning take first two numbers are; Then do division operation i.e 12)15(1 12 ________ 03)12(4 12 _________ 0(remainder ) If remainder becomes 0,then take divisor of last operation, i.e 3 Now division operation b/ w 3 and 20 3)20(6 18 ____ 2)3(1 2 ______ 1)2(2 2 ____ 0 Similarly now proceed with 1 n 54 1)54(54 54 ___ 0

.: last divisor 1 is the required H.C.F.

Jancy said: (Dec 27, 2017)

Divide the series by 3 I get 4 5 20 18.

Further divide by a 4, 1 5 5 18. Again divide by 5 I end up with 1 1 1 18 now I get lcm = 1080. Am I right?

Felix Vargees said: (Jan 15, 2018)
Why are we adding 8 with the lcm I don't get that because in some cases we do subtract the remainder from the lcm so could someone please help me out with this?

Ayush said: (Sep 22, 2018)
Can anyone tell me what is the smallest number which when divided by 12, 20, 36 leaves no remainder? Please answer it.

Fia said: (Dec 5, 2018)
What if it is to find the least number which when divided by 8, 12, 16 leaves remainder 7 in each case? Please, anyone, tell me.