CompanyName LCM and HCF Problems with Solutions

As we know that LCM * HCF = Product of two Numbers

Thus a + b = 55 and ab = 5 x 120 = 600

Thus 1/a + 1/b = (b + a)/(ab) = 55/600 = 11/120

Option D

Explanation:

L.C.M. of 21, 36, 66 = 2772

Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11

To make it a perfect square, it must be multiplied by 7 x 11.

So, required number = 2 x 2 x 3 x 3 x 7 x 7 x 11 x 11 = 213444

1024 is divisible by all numbers except 124

Answer: Option C

Explanation:

For any this type of question, remember
Product of two numbers = Product of their HCF and LCM

So Other number = (693*11)/99 = 77

We need to find out the HCF for given length.
15 meter 75 cm = 1575 cm.
11 meter 25 cm = 1125 cm
7 meter 65 cm = 765 cm.
1575 = 5 *5 *3 *3 *7
1125 = 5 *5 *5 *3 *3
765 = 5 *3 *3 *17

HCF of 1575, 1125 and 765 is 45 (5 *3*3).

In this type of question, its obvious we need to calculate the HCF, trick is
HCF of (1661 - 10) and (2045 -13)
= HCF (1651, 2032) = 127

LCM of 2-4-6-8-10-12 is 120 seconds, that is 2 minutes.

this means that all the bells ring together in every 2 minutes

Now 60/2 = 30

Hence the bells ring 30 times in 60 mins

As given the questions these numbers are co primes, so there is only 1 as their
common factor.
It is also given that two products have the middle number in common.
So, middle number = H.C.F. of 551 and 1073 = 29;

So first number is : 551/29 = 19
Third number = 1073/29 = 37

So sum of these numbers is = (19 + 29 + 37) = 85

LCM of 18, 24 and 32:

18 = 2 x 3 x 3
24 = 2 x 2 x 2 x 3
32 = 2 x 2 x 2 x 2 x 2
LCM = 2 x 2 x 2 x 2 x 2 x 3 x 3 = 288

The smallest four digit number that is divisible by 288:

288 x 3 = 864

288 x 4 = 1152

Since 288 is divisible by 18, 24 and 32, 1152 is also divisible by all
these numbers.

Therefore, 1152 is the smallest four digit number divisible by 18, 24 and 32.

Take the lcm of 3,4,5,6.
3=3×1
4=2×2
5=5×1
6=2×3
LCM=2×2×3×5=60

Therefore 60 is the number that is completely divisible by these numbers.
But we have to find the smallest number that leaves remainder 2.

Answer : 60 + 2=62