100+ HCF and LCM Questions and Answers for SSC Exams - 1

Question: 1

Which greatest number will divide 3026 and 5063 leaving remainders 11 and 13 respectively?

(A) 10

(B) 25

(D) 45

Ans: D

Required number = H.C.F. of (3026 – 11) and (5053 – 13)

= H.C.F. of 3015 and 5040 = 45.

Question: 2

The least number which when increased by 5 is divisible by each one of 24, 32, 36 and 54 is

(A) 859

(B) 869

(D) 4520

Ans: A

Required number = (L.C.M. of 24, 32, 36, 54) – 5 = 864 – 5 = 859.

Question: 3

Find the two largest numbers of four digits having 531 as their H.C.F.

(A) 9027, 9558

(B) 9037, 9568

(D) 9231, 9762

Ans: A

The greatest number of four digits divisible by 531 is 9558, so the other number is 9558 – 531 = 9027.

Thus, the numbers are 9558 and 9027.

Question: 4

What is the least number of cut pieces of equal length that can be cut of two lengths 10 m 857 mm and 15 m 87 mm?

(A) 164

(B) 172

(D) 194

Ans: C

H.C.F. of 10857 and 15087 is 141.

The least number of cut pieces = $$({10857 + 15087}) / {141})$$ = 184.

Question: 5

The greatest number that will divided 187, 233 and 279 leaving the same remainder in each case is

(A) 30

(B) 34

(D) 46

Ans: D

Required number = HCF of (223 – 187), (279 – 233) and (279 – 187)

= HCF of 46, 46 and 92 = 46.

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