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# H.C.F and L.C.M Questions

Home > Quantitative Aptitude > H.C.F and L.C.M > General Questions
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Let p and q be two prime numbers such that p is greater than q. If 319 is their LCM then the difference of thrice of q and p is:

A1

B0

C4

D9

Explanation:

Solution: We know that HCF of two prime numbers is 1.

Product of HCF and LCM = 1 x 319 = 319.

Remember that, Product of two number = Product of their HCF and LCM

pq = 319

Now, co-primes with product 319 are (1,319) and (29,11)

Since p > q, p = 29 and q = 11

Then 3q - p = 3 - 29 = 4.

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Find the largest 4-digit number, which gives the remainder 7 and 13 when divided by 11 and 17?

A9900

B9907

C9807

DNone of these

Explanation:

LCM of 11 and 17 = 187.
When divided by 11 remainder 7,so difference 4.
When devided by 17 remainder 13,so difference 4.
Largest no exactly devide by 11 & 17=9911
The no's = 9911-4 = 9907.

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The ratio of two numbers is 3:4 and their HCF is 4.Their LCM is:

A12

B16

C24

D48

Explanation:

Given Two No, ratio = 3:4 and their HCF = 4
So, No. = 3*4 =12 and 4*4=16
LCM of 12,16 = 48

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If an integer k is divisible by 2,5 and 13, what is the next largest number that is divisible by all the three given numbers ?

Ak+130

Bk+13

C2k+13

D2k+65

E2k

Explanation:

k+ LCM of 2,5,13
=> (k + 130)

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What is the least amount that a person can have, such that when he distributes it into groups of Rs.16 or Rs. 18 or Rs. 20 or Rs. 25, he is always left with Rs. 4?

ARs. 1796

BRs. 1804

CRs. 2596

DRs. 3604

Explanation:

Find the lcm of 16 18 20 and 25 i.e 3600.
so the amount is (3600 + 4) = Rs. 3604

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In a circular racetrack of length 100 m, three persons A, B and C start together. A and B start in the same direction at speeds of 10 m/s and 8 m/s respectively. While C runs in the opposite at 15 m/s. When will all the three meet for the first time after the start?

A100

B120

C110

D150

Explanation:

Since the track is a circular track A and B will meet every 50 seconds. i.e. 100 / (10-8).
Since it is a multiple of 50 they will be meeting at the starting point every 50 Seconds.
If you multiply 15 x 50 you will get 750 and after the second 50 it will be 1500.
All of them will meet at the starting point after 100

Workspace

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