Aptitude - Problems on H.C.F and L.C.M - Discussion
Discussion Forum : Problems on H.C.F and L.C.M - General Questions (Q.No. 7)
7.
Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:
Answer: Option
Explanation:
Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x.
So, 60x = 2400 or x = 40.
The numbers are (3 x 40), (4 x 40) and (5 x 40).
Hence, required H.C.F. = 40.
Discussion:
41 comments Page 1 of 5.
Mayur said:
3 years ago
Let's remember the common formula to find HCF or LCM whenever "ratio" is given,
LCM= LCM of ratio x HCF.
2400(given) = 60 x HCF,
HCF = 40.
LCM= LCM of ratio x HCF.
2400(given) = 60 x HCF,
HCF = 40.
(26)
Purushotham said:
3 years ago
2400/3 * 4 * 5 = 40.
(24)
Jayasri said:
5 years ago
Given the numbers are in ratio 3:4:5 so the actual numbers will be 3k,4k,5k.
Multiplication of all the numbers = h.c.f*l.cm.
H.c.f will be k and given l.c.m is 2400,
Therefore,3k * 4k * 5k = k * 2400,
By solving this we will get k = 40.
Multiplication of all the numbers = h.c.f*l.cm.
H.c.f will be k and given l.c.m is 2400,
Therefore,3k * 4k * 5k = k * 2400,
By solving this we will get k = 40.
(7)
Aryabhatta said:
3 years ago
Let number be 3a, 4a and 5a.
3 = 3 x 1
4 = 2 x 2
5 = 5 x 1.
LCM(3,4,5) = 3 x 2^2 * 5 = 60.
60a = 2400,
a= 40.
Now, Numbers are 120, 160, 200.
120 = 2^3 * 5 * 3.
160 = 2^5 * 5,
200 = 2 ^3 * 5^2.
HCF(120,160,200) = 2^3* 5^2 = 200.
3 = 3 x 1
4 = 2 x 2
5 = 5 x 1.
LCM(3,4,5) = 3 x 2^2 * 5 = 60.
60a = 2400,
a= 40.
Now, Numbers are 120, 160, 200.
120 = 2^3 * 5 * 3.
160 = 2^5 * 5,
200 = 2 ^3 * 5^2.
HCF(120,160,200) = 2^3* 5^2 = 200.
(6)
Harshitha Reddy said:
4 years ago
3x, 4x, 5x take LCM of these numbers is 60.
Formula:-numbers=LCM * hcf.
60x = 2400 * hcf,
X = 2400/60,
X = 40.
Formula:-numbers=LCM * hcf.
60x = 2400 * hcf,
X = 2400/60,
X = 40.
(3)
Khagendra Thapa Kazzi said:
2 months ago
Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x.
So, 60x = 2400 or x = 40.
Hence, the required H.C.F. = 40.
Then, their L.C.M. = 60x.
So, 60x = 2400 or x = 40.
Hence, the required H.C.F. = 40.
(2)
Sanju said:
2 years ago
Can someone explain these?
Factors of 4 : 1,2,4
Factors of 40 : 1,2,4,5,8,10,20,40
Therefore HCF is 4.
But we should only take pairs if 3,40 are co-primes means their HCF should be 1.
Here HCF should be 1 but it is 4.
Factors of 4 : 1,2,4
Factors of 40 : 1,2,4,5,8,10,20,40
Therefore HCF is 4.
But we should only take pairs if 3,40 are co-primes means their HCF should be 1.
Here HCF should be 1 but it is 4.
(2)
Devraj chapagain said:
8 years ago
LCM = HCF*remaining factors.
or, 2400 = HCF *3 *4*5.
So, HCF = 2400÷60.
= 40.
or, 2400 = HCF *3 *4*5.
So, HCF = 2400÷60.
= 40.
(2)
Vinay gudipati said:
7 years ago
Given the ratio is 3:4:5.
Consider the HCF of the three numbers is x i.e., is 3x, 4x, 5x.
LCM of 3x, 4x, 5x=60x.
Given that LCM of the three numbers is 2400.
Therefore 60x=2400.
x=40.
So the HCF value is 40.
Consider the HCF of the three numbers is x i.e., is 3x, 4x, 5x.
LCM of 3x, 4x, 5x=60x.
Given that LCM of the three numbers is 2400.
Therefore 60x=2400.
x=40.
So the HCF value is 40.
(1)
Balachandra said:
8 years ago
2400/3 = 800
2400/4 = 600
2400/5 = 480
HCF of 800, 600.480 is 40.
2400/4 = 600
2400/5 = 480
HCF of 800, 600.480 is 40.
(1)
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