LCM and HCF Quiz-1

1024 is divisible by all numbers except 124

Option C

Explanation:

L.C.M. of 20, 35, 65 = 1820

Now, 1820= 5 x 4 x 7 x 13

To make it a perfect square, it must be multiplied by 5 x 4 x 7 x 13

So, required number =5 x 4 x 7 x 13 x 5 x 4 x 7 x 13 = 3312400

Explanation:

According to the formula,
Product of two numbers = Product of their HCF and LCM

So Other number = Product of HCF and LCM/One Number = (369*27)/9 = 1107

 

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

We need to find out the HCF for given length.
20 meter 15 cm = 2015 cm.
21 meter 55 cm = 2155 cm
12 meter 65 cm = 1265 cm.
HCF of 2015, 2155 and 1265 is 5.

LCM of 3-6-9-12-15 is 180 hours

Now 360/180 = 2

Hence the clothes will be dries 2 times in 360 hours

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 399 and 525 = 21;

So first number is : 399/21 = 19
Third number = 525/21 = 25

So sum of these numbers is = (19 + 21 + 25) = 65

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

Thus a + b = 11 and ab = 1 x 30 = 30

Thus\frac{1}{a}+\frac{1}{b}=\frac{b+a}{ab}=\frac{11}{30}

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

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.