HCF and LCM TNPSC Previous Year Questions - 1

Question: 1

Even numbers are formed by taking at least two at a time from the numbers 0, 4, 8, 9. Their H.C.F is

(A) 1

(B) 2

(D) 6

View Answer

Ans: B

Since all the numbers formed are even, 2 is a common factor.

Also, H.C.F. of two of the numbers i.e., 48 and 490, is 2.

So, the H.C.F. of all the numbers formed is 2.

Question: 2

Three numbers are in the ratio 1 : 2: 3 and their H.C.F. is 12. The numbers are

(A) 4, 8, 12

(B) 5, 10, 15

(D) 10, 20, 30

View Answer

Ans: C

Let the required numbers be x, 2x and 3x.

Then, their H.C.F. = x. So, x = 12.

∴ The numbers are 12, 24 and 36.

Question: 3

Three numbers are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is

(A) 20

(B) 40

(D) 70

View Answer

Ans: B

Let the numbers be 3x, 4x and 5x.

Then, their L.C.M. = 60x.

So, 60x = 2400 or x = 40.

The numbers are (3 × 40), (4 × 40) and (5 × 40).

Hence, required H.C.F. = 40.

Question: 4

Let N ne the greatest number that will divide 1305, 4664 and 6905, leaving the same remainder in each case. Then sum of the digits in N is

(A) 2

(B) 4

(D) 6

View Answer

Ans: B

N = H.C.F. of (4665 – 1305), (6905 - 4665) and (6905 – 1305)

= H.C.F. of 3360, 2240 and 5600 = 1120.

Sum of digits in N = (1 + 1 + 2+ 0) = 4.

Question: 5

If three numbers are 2a, 5a and 7a, what will be their L.C.M.?

(A) 65a

(B) 70a

(D) 73a

View Answer

Ans: B

The given three numbers are 2a, 5a and 7a.

LCM of 2a, 5a and 7a = 2 × 5 × 7 × a = 70a.

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HCF and LCM TNPSC Previous Year Questions - 1

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