Question

The product of two numbers is 750 and their LCM is 150. Their HCF is: a. 1 b. 3 c. 5 d. 7

Answer 1

Answer:

c. 5

Step-by-step explanation:

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Answer 2

Answer :–

• Option (c) 5 is the correct answer.

Given :–

• The product of two numbers = 750
• Least Common Multiple (L.C.M.) = 150.

To Find :–

• Highest Common Factor (H.C.F.) ?

Formula Applied :–

• L.C.M. × H.C.F. = Product of two numbers.

Solution :–

L.C.M. × H.C.F. = Product of two numbers

Here, already given the value LCM and Product of two numbers,

1. LCM = 150
2. Product of two numbers = 750

So,

⟹ 150 × H.C.F. = 750

Now, turn L.H.S. to R.H.S.,

So, we turn L.C.M. (150) to the R.H.S. (750) and it will get divided in the R.H.S.

We turn L.C.M. (150) because we need to find the value of H.C.F.,

So,

⟹ H.C.F. = $\dfrac{75 \cancel0}{15 \cancel0}$

Cancel the denominator's 0 and the numerator's 0, we obtain

⟹ H.C.F. = $\dfrac{\cancel{75}}{\cancel{15}}$

Cut the denominator and the numerator by 5, we obtain

⟹ H.C.F. $\dfrac {\cancel{15}}{\cancel3}$

Now, cut the denominator and the numerator by 3, we obtain

⟹ H.C.F. = 5

Hence,

Option (c) is the correct option.