Question

16.If the product of two numbers is 1050 and their HCF is 25, find their LCM.

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Answer 1

✬ $\large\orange{\texttt{LCM = 42}}$ ✬

Explanation:

Given:

• Product of two numbers is 1050.
• Their HCF is 25.

To Find:

• What is their LCM ?

Solution: Let the LCM be L. As we know that the

★ LCM $\times$ HCF = Product of two numbers ★

A/q

• HCF is 25 & Product is 1050.

$\implies{\rm }$ LCM $\times$ 25 = 1050

$\implies{\rm }$ L $\times$ 25 = 1050

$\implies{\rm }$ 25L = 1050

$\implies{\rm }$ L = $\bf\dfrac{1050}{25}$

$\implies{\rm }$ L = 42

Hence, Their LCM is 42.

_________________

★ Verification ★

➪ $\large\pink{\texttt {HCF x LCM = 1050}}$

➪ $\large\pink{\texttt {25 x 42 = 1050}}$

➪ $\large\pink{\texttt {1050 = 1050}}$

$\large\boxed{\texttt{Verified}}$

Answer 2

$\huge\mathfrak{Answer:}$

HCF (Highest Common Factor) :

• It is the product of smaller power of each common prime factor in the numbers.

LCM (Least Common Multiple) :

• It is the product of the greatest power of each prime factor involved in the numbers.

Given:

• We have been given that the product of two numbers is 1050.
• HCF of these numbers is 25.

To Find:

• We need to find the LCM of these numbers.

Solution:

It is given that the product of two numbers is 1050 and their HCF is 25.

We know that HCF × LCM = Product of numbers.

Substituting the values, we have

=> 25 × LCM = 1050

=> LCM = 1050/25

=> LCM = 42

Therefore, the LCM of the two numbers is 42.