Method of Finding LCM

Q.

$4$ Bells toll together at $9:00\mathrm{A}.\mathrm{M}.$ They toll after $7,8,11$ and $12$ $\mathrm{seconds}$ respectively. How many times will they toll together again in the next $3$ hour?

Q.

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

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

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

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

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

Q.

What is the lcm of $60$ and $75$?

Q.

Find the LCM and HCF of the following integers by applying the prime factorization method : 8, 9 and 25

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

Q.

The LCM of$60,80,108.$

Q.

Find the LCM and HCF of 510 and 92 and verify that LCM.HCF = product of the two numbers. [4 MARKS]

Q. Simplify using laws of exponents : $\frac{100\times 3^3\times 25\times 32}{5^2\times 2^4\times 10}$

Q.

Question 12
On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk, so that each can cover the same distance in complete steps?

Q. $1$ $3$
$5$ $7$ $9$ $11$

Q. Arrange the following in ascending order of magnitude:

(i) $\sqrt[3]{4},\sqrt[4]{5},\sqrt{3}$

Q. Which number can replace both question marks in the equation $\frac{4\frac{1}{2}}{?}=\frac{?}{32}$.

1. 12
2. 7
3. $7\frac{1}{2}$
4. None of these

Q. Use the law of exponents and simplify:
$\frac{3^{-4}\times {10}^{-5}\times \left(625\right)}{5^{-3}\times 6^{-4}}$

Q. ${}^n{P}_4=20\times {}^n{P}_2$ find $n$

Q.

Question 98

In the following question, state whether the given statement is true (T) or false (F).
The LCM of two coprime numbers is equal to product of the numbers.

Q.

Write the H.C.F of the smallest composite number and the
smallest prime number.