Most Important Questions with Short Tricks on L.C.M & H.C.F For SSC Exams

Most Important Questions with Short Tricks on L.C.M & H.C.F For SSC Exams

Question 1: The HCF and LCM of two numbers are 12 and 72 respectively. If the sum of two numbers is 60, then one of the number is

(A)  24

(B)  36

(C)  either (A) or (B)

(D)   Can't be determined

Solution:

Let the number are 12 x and 12 y, where x and y are co-prime to each other.

Question 2: Find the greatest number of six digits which, on being divided by 6, 7, 8, 9 and 10 leaves 4, 5, 6, 7 and 8 as remainders respectively.

(A)  997868

(B)  996878

(C)  996786

(D)  997918

Solution: 

The LCM of 6,  7, 8, 9 and 10 = 2520

The greatest number of 6 digits = 999999

Dividing 999999 by 2520, we get 2079 as remainder.

Hence, the 6-digit number divisible by 2520 is = 999999 – 2079 = 997920

Since, 6 – 4 = 2, 7 – 5 = 2, 8 – 6 = 2, 9 – 7 = 2, 10 – 8 = 2, then remainder in each case is less than the divisor by 2.

The required number = 997920 – 2 = 997918

Question 3 : Find the greatest number by which 78, 153 and 228 will be divided so that it leaves the same remainder in every case?

(A)  25

(B) 75

(C) 77

(D) 76

Solution:

Required number = HCF of {(153 – 78), (228 – 153) and (228 – 78)} = H.C.F. of (75, 75, 150) = 75

Question 4: What is the smallest sum of money which contains Rs 2.50, Rs 20, Rs 1.20 and Rs 7.50?

(A)  Rs 40

(B)  Rs 50

(C)  Rs 60

(D)  Rs 70

Solution:

LCM of 2.50, 20, 1.20 and 7.50 = (LCM of 25, 200, 12 and 75) x 0.1

= 600 x 0.1   = Rs  60

Question 5:  Find the least number of square tiles required to pave the ceiling of a hall 15 m 17 cm long and 9 m 2 cm broad.

(A)    814

(B)    816

(C)     818

(D)     820

Solution:

Side of tile = HCF of 1517 cms and 902 cms = 41 cms

Area of each tile = 41 x 41 cm2

The number of tiles =