The Fundamental Theorem of Arithmetic

Q. If the HCF of 306 and 657 is 9, then the LCM of 306 and 657 will be .

1. 22338
2. 22348
3. 657

Q.

Find the HCF of $96$ and $404$ by prime factorization and use it to find the LCM.

Q. Question 3 (i)
Find the LCM and HCF of 12, 15 and 21 by applying the prime factorization method.

Q. If p is a prime number then find the LCM of p, p^{​​​​​​2} and p^{​​​​​​3}

Q.

Find the LCM and HCF of 12, 15 and 21 by applying the prime factorization method. [2 MARKS]

Q. Find LCM and HCF of 3930 and 1800 by prime factorisation method.

Q.

If $\mathrm{HCF}(336,54)=6$, then find the $\mathrm{LCM}(336,54)$.

Q. Find the HCF and LCM of 90 and 144 by prime factorisation method.

1. 18 and 720
2. 720 and 18
3. 360 and 180
4. 180 and 720

Q. If two positive integers p and q can be written $p=a^{2}b$ and $q=a{b}^2$ , where p and q are prime numbers, then the LCM(p, q) is .

1. $a{b}^2$
2. $a^2{b}^2$
3. $ab$
4. $a^{2}b$

Q.

If $3$ is the least prime factor of number $a$ and $7$ is the least prime factor of number $b$, then the least prime factor of $a+b$ is

1. $2$

2. $3$

3. $5$

4. $10$

Q.

Find the HCF and LCM of $306$and $657$ by prime factorization method.

Q. In a seminar, the number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively. Find the minimum number of rooms required if in each room the same number of participants are to be seated and all of them being in the same subject. [4 MARKS]

Q. Find the HCF and LCM of 90 and 144 by prime factorisation method.

1. 720 and 18
2. 360 and 180
3. 18 and 720
4. 180 and 720

Q. is the product of the greatest power of each prime factor, involved in the numbers.

1. HCF
2. LCM
3. Composite number

Q.

$15$ pastries and $12$ biscuit packets have been donated for a school fete. These are to be packed in several smaller identical boxes with the same number of pastries and biscuit packets in each. How many biscuit and how many pastries will each box contain?

Q. In a seminar, the number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively. Find the minimum number of rooms required if in each room the same number of participants are to be seated and all of them being in the same subject. [4 MARKS]

Q. Question 3 (ii)
Find the LCM and HCF of 17, 23 and 29 by applying the prime factorization method.

Q. Question 3 (i)
Find the LCM and HCF of 12, 15 and 21 by applying the prime factorization method.

Q. Question 3 (ii)
Find the LCM and HCF of 17, 23 and 29 by applying the prime factorization method.

Q.

$\text{If the number}{\mathrm{1.2.2}}^2{.2}^3{.2}^4..........{.2}^{20}.{3.3}^2{.3}^3{.3}^4.......{.3}^{10}$
$\text{is written in power of '6' then the highest}$
$\text{power of '6' is \_\_\_\_\_}.$

1. 10

2. 20

3. 30

4. 55

Q. Question 3 (iii)
Find the LCM and HCF of 8, 9 and 25 by applying the prime factorization method.

Q. In a seminar, the number of participants for the subjects Hindi, English and Mathematics are 60, 84 and 108 respectively. Find the minimum number of rooms required if in each room the same number of participants are to be seated and all of them are for the same subject.

1. 7
2. 14
3. 21
4. 28

Q. Find the LCM and HCF of 8, 9 and 25 by applying the prime factorization method.

Q. If a = $2^3\times 3$, b = $2\times 3\times 5$, c = $3^n\times 5$ and LCM (a, b, c) = $2^3\times 3^2\times 5$, then n = ?
(Here, n is a natural number)

1. 1
2. 2
3. 3
4. 4

Q. If two positive integers p and q can be written $p=a^{2}b$ and $q=a{b}^2$ , where p and q are prime numbers, then the LCM(p, q) is .

1. $a^2{b}^2$
2. $a{b}^2$
3. $a^{2}b$
4. $ab$

Q. Question 3 (i)
Find the LCM and HCF of 12, 15 and 21 by applying the prime factorization method.

Q. Find the LCM and HCF of 17, 23 and 29 by applying the prime factorization method.

Q.

Find the least number which when divided by $10,15,30$ and $60$ leaves remainder $9$ in each case

Q. If $n$ is any natural number, then $9^n-5^n$ may end with ___________.

1. 3
2. 6
3. 5
4. 8

Q.

If $a=2^3\times 3^4\times 7^2$and $b=2^3\times 3^2\times 5^3,$ then which of the following is true?

1. $HCF=2^3\times 3^2;LCM=2^3\times 3^4\times 5^3\times 7^2$
2. $HCF=2^3\times 3^2;LCM=2^3\times 3^2\times 5^2\times 7^3$
3. $LCM=2^2\times 3^2;HCF=2^3\times 3^3\times 5^3\times 7^2$
4. $HCF=2^3\times 3^2;LCM=2^3\times 3^2\times 5^3\times 7^3$