Test: LCM & GCD - 3 - GMAT MCQ

Since we need total number of books, we must find LCM of 4,5,9,10

Numerators = 36, 48 and 72.
72 is largest number among them. 72 is not divisible by 36 or 48
Start with table of 72.
72 x 2 = 144 = divisible by 72, 36 and 48
∴ LCM of numerators =144
Denominators= 225, 150 and 65.
We can see that they can be divided by 5.
On dividing by 5 Imeget 45, 30 and 13
We cannot divide further. So, HCF = GCD =5 

Wall can be covered only by using square sized wallpaper pieces.
Different sized squares are not allowed.
Length = 4 m 50 cm = 450 cm ; Height = 3 m 50 cm = 350 cm
Maximum square size of possible means HCF of 350 and 450
We can see that 350 and 450 can be divided by 50.
On dividing by 50, we get 7 and 9.
Since we cannot divide further, HCF = 50 = size of side of square 

Since we require minimum number of square tiles, the size of the tile is given as the H.C.F. of two sides of the room. The H.C.F. Of 1625 cm & 1275 cm. is 25 cms. Hence, we get,
Required Number = (1625 * 1275) / (25 * 25) = 3315

Let the numbers be 4x and 5x.
Then, their L.C.M. = 20x. 
20x = 60 or x = 3.
The numbers are 12 and 15.
Hence, required sum = (12 + 15) = 27.

Given numbers are 2.00, 2.70 and 0.09.
L.C.M. of 200, 270 and 9 is 5400.
L.C.M. Of given numbers = 54.00 = 54

L.C.M of 5, 4, and 2 = 20. On dividing 2430 by 20, the remainder is 10.
Therefore, number to be added = (20 - 10) = 10

Let the numbers be 4x and 5x.

H.C.F = x. So, x=4.
So, the numbers are 16 and 20
L.C.M of 16 and 20 = 80.

The largest size of the tile is H.C.F. of 480 cm and 538 cm is 2 cm.

The L.C.M. of 12, 20 and 35 is 420. Hence, all 3 bells beep together after 420 minutes = 7 hours
Hence, the 3 bells will beep together 7 hours after 10 a.m. i.e. at 5 p.m.

The L.C.M. of 3, 5 and 9 is 45.
Hence, the number is of the form (45a + 2).
The least value of ‘a’ for which (45a + 2) is multiple of 11 is 9.
Therefore, the number is 407.

It is given that sum of two numbers is 100. Let the two numbers be x and 100 – x and HCF is 5 and LCM is 495

=> We need to apply the formula: HCF x LCM = Product of two numbers

Which gives x(100 – x) = 495 x 5

Solving the equation we get a quadratic which looks like this:

Therefore, Two numbers are 55 and 45