HCF & LCM MCQs for Competitive Examination
Solve the following problems.
Q. 1
What is the HCF of (23 * 34)and (25 * 32)?
(A) 25 * 33
(B) 23 * 34
(C) 23 * 32
(D) 25 * 34
Answer: (C) 23 * 32
Explanation: N/A
Q. 2
The HCF and LCM of two numbers is 6 and 5040 respectively. If one of the numbers is 210, then other number is
(A) 170
(B) 144
(C) 156
(D) 196
Answer: (B) 144
Explanation: HCF * LCM = Product of the two numbers
Q. 3
What is the sum of digits of the least number, which when divided by 15, 18 and 24 leaves the remainder 8 in each case and is also divisible by 23?
(A) 17
(B) 16
(C) 15
(D) 18
Answer: (A) 17
Explanation: The required number is = LCM(15, 18, 24) + 8 = 368, which is divisible by 23. The sum of the digits of 368 is 17
Q. 4
What is the largest 4 digit number, which when divided by 4, 5, 6 and 7 leaves remainder as 2, 3, 4 and 5 respectively?
(A) 9999
(B) 9960
(C) 9658
(D) 9668
Answer: (C) 9658
Explanation: LCM(4, 5, 6, 7) = 420
Now, the largest 4 digits number = 9999
Dividing, 9999 by 499 we have 339 as remainder. Therefore the largest 4 digits number that is divisible by 4, 5, 6 and 7 is = (9999 – 339) = 9660
Also, (4 – 2) = (5 – 3) = (6 – 4) = (7 – 5) = 2
Hence the required number = 9660 – 2 = 9658
Q. 5
What least value which should be added to 1812 to make it divisible by 7, 11 and 14?
(A) 12
(B) 36
(C) 72
(D) 154
Answer: (B) 36
Explanation: LCM (7, 11, 14) =154
Dividing 1812 by 154 we have 118 as remainder. Hence we have to add (154 – 118) = 36 to 1812 to make it divisible by 7, 11 and 14
Q. 6
The LCM of two numbers is 2079 and their HCF is 27. If one of the numbers is 189, the other number is
(A) 297
(B) 584
(C) 189
(D) 216
Answer: (A) 297
Explanation: N/A
Q. 7
The product of two numbers is 2160 and their HCF is 12. The number of such possible pairs is
(A) 1
(B) 2
(C) 3
(D) 4
Answer: (B) 2
Explanation: Let the two numbers be 12x and 12y (where x and y are coprime)
Now, 12x * 12y = 2160 or xy = 15
15 = 1 * 15 = 3 * 5
Possible pairs (12 * 1, 12 * 15) and (12 * 3, 12 * 5) = (12, 180) and (36 and 60)
Q. 8
The product of two co-prime numbers is 117. Then their LCM is
(A) 117
(B) 9
(C) 13
(D) 39
Answer: (A) 117
Explanation: N/A
Q. 9
The LCM of three different numbers is 120. Which of the following cannot be their HCF?
(A) 8
(B) 12
(C) 24
(D) 35
Answer: (D) 35
Explanation: N/A
Q. 10
The HCF and LCM of two numbers are 12 and 924 respectively. Then the number of such pairs is
(A) 0
(B) 1
(C) 2
(D) 3
Answer: (C) 2
Explanation: Let the two numbers be 12x and 12y
Hence, 12xy = 924 or xy = 77
There are only two such pairs.
Q. 11
The LCM of two numbers is 4 times their HCF. The sum of LCM and HCF is 125. If one of the numbers is 100, then the other number is
(A) 5
(B) 25
(C) 100
(D) 125
Answer: (B) 25
Explanation: LCM =4 * HCF, and, LCM + HCF = 125
Solving, we have HCF = 25, LCM = 100
Again, LCM * HCF = Product of the two numbers
Putting the values we have the required number = 25
Q. 12
Three men step off together from the same spot. Their steps measure 63 cm, 70 cm and 77 cm respectively. The minimum distance each should cover so that all can cover the distance in complete steps is
(A) 9630 cm
(B) 9360 cm
(C) 6930 cm
(D) 6950 cm
Answer: (C) 6930 cm
Explanation: Required distance = LCM(63, 70, 77) = 6930 cm
Q. 13
Find the least number which when divided separately by 15, 20, 36 and 48 leaves 3 as remainder in each case.
(A) 183
(B) 243
(C) 483
(D) 723
Answer: (D) 723
Explanation: N/A
Q. 14
LCM of (2/3), (4/9), (5/6) and (7/12) is
(A) 1/3
(B) 20/3
(C) 140/18
(D) 140/3
Answer: (C) 140/3
Explanation: LCM of (2/3), (4/9), (5/6) and (7/12) = LCM(2, 4, 5, 7)/HCF(3, 9, 6, 12) = 140/3
Q. 15
The greatest 4-digit number exactly divisible by 10, 15, 20 is
(A) 9990
(B) 9960
(C) 9980
(D) 9995
Answer: (B) 9960
Explanation: N/A
Q. 16
The bells begin to toll together and they toll respectively at intervals of 6, 7, 8, 9 and 12 seconds. After how many seconds will they toll together again?
(A) 72 seconds
(B) 612 seconds
(C) 504 seconds
(D) 318 seconds
Answer: (C) 504 seconds
Explanation: N/A
Q. 17
The HCF and LCM of two numbers are 44 and 264 respectively. If the first number is divided by 2, the quotient is 44. The other number is
(A) 147
(B) 528
(C) 132
(D) 264
Answer: (C) 132
Explanation: The first number is 44 * 2 = 88
The second number = (44 * 264)/88 = 132
Q. 18
The LCM of two prime numbers x and y (x > y) is 161. The value of (3y – x)
(A) – 2
(B) – 1
(C) 1
(D) 2
Answer: (A) – 2
Explanation: xy = 161
x = 161, y = 1 and x = 23, y = 7 (x > y)
Since x and y are prime, hence the value of x and y will be 23 and 7 respectively
(3y – x) = – 2
Q. 19
What is the LCM of 120 and 450?
(A) 2400
(B) 1800
(C) 3600
(D) 4800
Answer: (B) 1800
Explanation: N/A
Q. 20
How many numbers are there from 300 to 700, which are divisible by 2, 3 and 7?
(A) 7
(B) 8
(C) 9
(D) 10
Answer: (C) 9
Explanation: N/A