Find the L C M and H C F of the following pairs of integers and verify that L C M × H C F = product of the two numbers. 510 and 92

Given numbers are 510 and 92 510 = 2 × 3 × 5 × 17 92 = 2 × 2 × 23 2 is the largest number which divides both 510 and 92 . So, HCF = 2 . L C M = 2 × 2 × 3 × 5 × 17 × 23 = 23460 Product of the two numbers = 510 × 92 = 46920 H C F × L C M = 2 × 23460 = 46920 Hence, the product of two numbers = H C F × L C M .

Find the L C M and H C F of the following pairs of integers and verify that L C M × H C F = product of the two numbers. 510 and 92

Given numbers are 510 and 92 510 = 2 × 3 × 5 × 17 92 = 2 × 2 × 23 2 is the largest number which divides both 510 and 92 . So, HCF = 2 . L C M = 2 × 2 × 3 × 5 × 17 × 23 = 23460 Product of the two numbers = 510 × 92 = 46920 H C F × L C M = 2 × 23460 = 46920 Hence, the product of two numbers = H C F × L C M .

Find the L C M and H C F of 336 and 54 and verify that L C M × H C F = product of the two numbers.

Given numbers are: 336 and 54 . 336 = 2 × 2 × 2 × 2 × 3 × 7 = 2 4 × 3 × 7 54 = 2 × 3 × 3 × 3 = 2 × 3 3 6 is the largest number which divides both 336 and 54 . So, HCF = 6 . L C M = 2 4 × 3 3 × 7 = 3024 . Verification: Product of the numbers = 336 × 54 = 18144 H C F × L C M = 6 × 3024 = 18144 Hence, the product of two numbers = H C F × L C M .

Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

There are two types of numbers, namely, prime and composite. Prime numbers have only two factors namely 1 and the number itself whereas composite numbers have factors other than 1 and itself. It can be observed that, 7 × 11 × 13 + 13 = 13 × ( 7 × 11 + 1 ) = 13 × ( 77 + 1 ) = 13 × 78 = 13 × 13 × 6 The given expression has 6 and 13 as its factors. Therefore, it is a composite number. 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 = 5 × ( 7 × 6 × 4 × 3 × 2 × 1 + 1 ) = 5 × ( 1008 + 1 ) = 5 × 1009 . 1009 cannot be factorized further. Therefore, the given expression has 5 and 1009 as its factors. Hence, it is a composite number.

E M B I B E

MATHEMATICS Textbook for Class X>Chapter 1 - Real Numbers>Exercise 1.2>Q 2

MEDIUM

10th Assam Board

IMPORTANT

Earn 100

Find the $L C M$ and $H C F$ of the following pairs of integers and verify that $L C M \times H C F =$ product of the two numbers.
$510$ and $92$

Important Questions on Real Numbers

MEDIUM

10th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 1 - Real Numbers>Exercise 1.2>Q 2

Find the

L C M

and

H C F

of

336

and

54

and verify that

L C M \times H C F =

product of the two numbers.

MEDIUM

10th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 1 - Real Numbers>Exercise 1.2>Q 3

Find the

L C M

and

H C F

of the following integers by applying the prime factorization method.

12, 15

and

21

MEDIUM

10th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 1 - Real Numbers>Exercise 1.2>Q 3

Find the

L C M

and

H C F

of the following integers by applying the prime factorization method.

17, 23

and

29

MEDIUM

10th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 1 - Real Numbers>Exercise 1.2>Q 3

Find the

L C M

and

H C F

of the following integers by applying the prime factorization method.

8, 9

and

25

MEDIUM

10th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 1 - Real Numbers>Exercise 1.2>Q 4

Given that

H C F (306, 657) = 9

, find

L C M (306, 657)

.

EASY

10th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 1 - Real Numbers>Exercise 1.2>Q 5

Check whether

6^{n}

can end with the digit

0

for any natural number

n

.

MEDIUM

10th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 1 - Real Numbers>Exercise 1.2>Q 6

Explain why

7 \times 11 \times 13 + 13

and

7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5

are composite numbers.

MEDIUM

10th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 1 - Real Numbers>Exercise 1.2>Q 7

There is a circular path around a sports field. Sonia takes

18

minutes to drive one round of the field, while Ravi takes

12

minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?