Using prime factorization, find the HCF and LCM of: 144, 198 - Vidyadip

Question

Using prime factorization, find the $HCF$ and $LCM$ of:
$144, 198$

✓

Answer

$144 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 = 2^4 \times 3^2$
$198 = 2 \times 3 \times 3 \times 11= 2 \times 3^2 \times 11$
$HCF (144, 198) = 2 \times 3^2 = 18$
$LCM (144, 198) = 2^4 \times 3^2 \times 11 = 1584$
$HCF \times LCM = 28512 144 \times 198 = 28512$
$\Rightarrow HCF \times LCM =$ product of given numbers Hence verified.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Real Numbers→Real Numbers — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

Give two different examples of each of the following:

similar figures.
non-similar figures.

The first term of an $A.P.$ is $5$, the last term is $45$ and the sum is $400$. Find the number of terms and the common difference.

Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5. Find the numbers.

A solid cuboid of iron with dimensions 53cm × 40cm × 15cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8cm and 7cm respectively. Find the length of pipe.

For the following arithmetic progressions write the first term a and the common difference d:
$-5, -1, 3, 7, ....$

The radii of the circular ends of a frustum of height 6cm are 1cm and 6cm, respectively. Find the slant height of the frustum.

A play ground has the shape of a rectangle, with two semi-circles on its smaller sides as diameters, added to its outside. If the sides of the rectangle are 36m and $24.5\ m$, find the area of the playground. $\Big(\text{Take }\pi=\frac{22}{7}\Big).$

Find n if the given value of x is the $n^{th}$ term of the given A.P.
$1,\frac{21}{11},\frac{31}{11},\frac{41}{11}, .....;\text{ x}=\frac{171}{11}.$

Cards marked with numbers 1, 3, 5, ..., 101 are placed in a bag and mixed thoroughly. A card is drawn at random from the bag. Find the probability that the number on the drawn card is:

Less than 19.
A prime number less than 20.

Find the area of triangle $\text{ABC}$ with $A (1,-4)$ and the mid$-$points of sides through $A$ being $(2,-1)$ and $(0,-1)$.