Problems on L.C.M and H.C.F

A. 180
B. 360
C. 540
D. 1260
Explanation:
4 * 27 * 3125 = 22 * 33 * 55;
8 * 9 * 25 * 7 = 23 * 32 * 52 * 7;
16 * 81 * 5 * 11 * 49 = 24 * 34 * 5 * 72 * 11
H.C.F = 22 * 32 * 5 = 180.

A. 13/16
B. 15/16
C. 17/26
D. 25/26
Explanation:
1095)1168(1
1095
———–
73)1095(15
1095
———-
0
So, H.C.F of 1095 and 1168 = 73.
1095/1168 = (1095/73) / (1168/73) = 15/16.

A. 99
B. 101
C. 176
D. 182
Explanation:
99 = 1 * 3 * 3 * 11; 101 = 1 * 101;
176 = 1 * 2 * 2 * 2 * 2 * 11; 182 = 1 * 2 * 7 * 13
So, divisors of 99 are 1, 3, 9, 11, 33 and 99;
divisors of 101 are 1 and 101;
divisors of 176 are 1, 2, 4, 8, 16, 22, 44, 88 and 176;
divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182.
Hence, 176 has the most number of divisors.

A. 2 * 2 * 3 * 3 * 7
B. 2 * 2 * 2 * 3 * 7
C. 3 * 3 * 3 * 3 * 7
D. 2 * 3 * 3 * 3 * 7

A. 35
B. 37
C. 42
D. 30
Explanation:
The number of liters in each can = HCF of 80, 144 and 368 = 16 liters.
Number of cans of Maaza = 80/16 = 5
Number of cans of Pepsi = 144/16 = 9
Number of cans of Sprite = 368/16 = 23
The total number of cans required = 5 + 9 + 23 = 37 cans.

A. 110
B. 124
C. 96
D. 117
Explanation:
Length = 6 m 24 cm = 624 cm
Width = 4 m 32 cm = 432 cm
HCF of 624 and 432 = 48
Number of square tiles required = (624 * 432)/(48 * 48) = 13 * 9 = 117

A. 3
B. 4
C. 5
D. 6
Explanation:
Calculate the differences, taking two numbers at a time as follows:
(215-47) = 168
(365-215) = 150
(365-47) = 318
HCF of 168, 150 and 318 we get 6, which is the greatest number, which while dividing 47, 215 and 365 gives the same remainder in each cases is 5.

A. 16
B. 17
C. 18
D. 19
Explanation:
Subtract the remainder 3 from each of the given numbers: (19-3)=16, (67-3)=64 and (83-3)=80. Now, find the HCF of the results 16, 64 and 80, we get 16. Thus, the greatest number is 16.

A. 5
B. 6
C. 7
D. 8
Explanation:
The greatest number that exactly divides 35, 91 and 840 is the HCF of the three numbers. So, calculating HCF we get the answer 7.

A. 1020
B. 1026
C. 1030
D. 1022
Explanation:
Lowest 4-digit number is 1000.
LCM of 3, 4 and 5 is 60.
Dividing 1000 by 60, we get the remainder 40. Thus, the lowest 4-digit number that exactly divisible by 3, 4 and 5 is 1000 + (60 – 40) = 1020.
Now, add the remainder 2 that’s required. Thus, the answer is 1022.