100+ HCF and LCM Questions and Answers for SSC Exams - 2
Question: 6
The greatest integer that divides 358, 374, 334 leaving the same remainder in each case is
(A) 5
(B) 6
(C) 7
(D) 9
Ans: B
Given numbers are 358, 376, 234.
Let us find the difference of numbers two by two.
376 – 358 = 18; 376 – 234 = 42
358 – 334 = 24
HCF of 42, 24, 18 = 6
Hence the required number is 6.
Question: 7
The L.C.M. of three different numbers is 120. Which of the following cannot be their H.C.F.?
(A) 8
(B) 12
(C) 24
(D) 35
Ans: D
Since H.C.F. is always a factor of L.C.M., we cannot have three numbers with H.C.F. 35 and L.C.M. 120.
Question: 8
The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is
(A) 25 cm
(B) 35 cm
(C) 45 cm
(D) 55 cm
Ans: C
Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm.
Question: 9
A rectangular courtyard 3.78 metres long and 5.25 metres wide is to be paved exactly with square tiles, all of the same size. What is the largest size of the tile which could be used for the purpose?
(A) 7 cm
(B) 14 cm
(C) 21 cm
(D) 42 cm
Ans: C
Largest size of the tile = H.C.F. of 378 cm and 525 cm = 21 cm.
Question: 10
The least number of five digits which is exactly divisible by 12, 15 and 18 is
(A) 10010
(B) 10070
(C) 10080
(D) 10090
Ans: C
Least number of 5 digits is 10000.
L.C.M. of 12, 15 and 18 is 180.
On dividing 10000 by 180, the remainder is 100.
∴ Required number = 10000 + (180 – 100) = 10080.
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