Question

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4. The product of two numbers is 2925 and their HCF IS 15. Find the LCM of these numbers​

Answer 1

Question:

• The product of two numbers is 2925 and their HCF is 15. Find LCM of these numbers.

Answer:

Given:

• Product of two number is 2925
• HCF of numbers is 15

To Find:

• LCM of numbers?

Solution:

In this question, we have given that product of two numbers is 2925 and their HCF is 15.

We know that:

• $\large{\boxed{\bf{Product~of~numbers~=~HCF\times~LCM}}}$

Where,

• Product of numbers = 2925 ••••(given)
• HCF = 15 •••••(given)
• LCM = x •••••(supposed)

Put values in formula :

$\small{\bf{Product~of~numbers~=~HCF\times~LCM}}$

$\implies\small{\bf{2925~=~15\times~x}}$

$\implies\small{\bf{2925~=~15x}}$

$\implies\small{\bf{x~=~\dfrac{2925}{15}}}$

$\implies\small{\bf{x~=~\cancel{\dfrac{2925}{15}}}}$

$\implies\small{\bf{x~=~195}}$

Therefore,

• $\large{\underline{\boxed{\red{\bf{LCM~of~number~=~195}}}}}$

Answer 2

$\large\sf\underline{Given\::}$

• Product of two numbers is 2925

• HCF is 15

‎

$\large\sf\underline{To\:find\::}$

• LCM of those numbers whose product is 2925

‎

$\large\sf\underline{Concept\:to\:be\:used\::}$

$\sf\:LCM~\times~HCF~=~Product~of~two~numbers$

‎

• LCM : Lowest Common Multiple

• HCF : Highest Common Factor

‎

$\large\sf\underline{Solution\::}$

Using the concept as mentioned earlier :

$\sf\color{gray}{\maltese}$ LCM × HCF = Product of two numbers

‎

Here :

• HCF = 15

• Product of the two numbers = 2925

‎

Substituting these values in the concept :

$\sf\to\:LCM~\times~15~=~2925$

Transposing 15 from LHS to RHS it goes to the denominator

$\sf\to\:LCM~=\frac{2925}{15}$

Reducing the fraction to the lower terms

$\sf\to\:LCM~=\cancel{\frac{2925}{15}}$

$\sf\to\:LCM~=\cancel{\frac{585}{3}}$

$\small{\underline{\boxed{\mathrm{\to\:LCM~=~195}}}}$ ★

__________________

Verification :-

LCM × HCF = Product of two numbers

‎

Here :

• LCM = 195
• HCF = 15
• Product of the two numbers = 2925

‎

Henceforth :

$\tt\dashrightarrow\:195 \times 15 = 2925$

$\tt\dashrightarrow\:2925= 2925$

$\tt\dashrightarrow\:LHS~=~RHS$

Hence Verified !~

__________________

$\dag\:\underline{\sf So\:the\:required\:LCM\:is\:195}$ .

‎