can two numbers have 18 as their hcf and 380 as their lcm? give reasons.

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Question 8 Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.

Question 8 Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.

Byju's Answer Standard X Mathematics

Applications of HCF & LCM in Real-World Problems

Question 8 Ca... Question Question 8

Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.

Open in App Solution

HCF is always a factor of LCM. Here, 18 is not a factor of 380. Thus, two numbers cannot have 18 as their HCF and 380 as their LCM.

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SIMILAR QUESTIONS

Q. Question 8

Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.

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Applications of HCF & LCM in Real-World Problems

Standard X Mathematics

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Can two numbers have 18 as their HCF and 380 as their LCM ? Give reason.

Click here👆to get an answer to your question ✍️ Can two numbers have 18 as their HCF and 380 as their LCM ? Give reason.

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>>Can two numbers have 18 as their HCF and

Question

Can two numbers have 18 as their HCF and 380 as their LCM ? Give reason.

Since HCF is 18 numbers can be assumed as 18x and 18y.

Hard Open in App Solution Verified by Toppr ⇒380=2×5×2×19

⇒380 is not divisible by 18 itself hence HCF 18 and LCM as 380 is not possible.

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Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons

Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons - No, two numbers cannot have 18 as their HCF and 380 as their LCM.

Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons

Solution:

No,

HCF is always a factor of LCM but 18 is not a factor of 380

Therefore, 18 is not a factor of 380.

✦ Try This: Can two numbers have 16 as their HCF and 380 as their LCM

We know that

The product of two numbers is equal to the product of their LCM and HCF

Consider a and b as the two numbers

a x b = HCF × LCM a × b = 16 × 380

For 16 to be the HCF of a and b, both a and b must be the multiple of 16.

Consider a as the smallest multiple of 16

16 × b = 16 × 380 b = 380. a = 16 and b = 380.

HCF of these two numbers is 4 and not 16

a cannot be equal to 16

If we consider any bigger multiple of 16, then we will arrive at a contradiction

Therefore, there cannot exist two natural numbers having 16 as their HCF and 380 as their LCM

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 1NCERT Exemplar Class 10 Maths Exercise 1.2 Problem 8

Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons

Summary:

No,two numbers cannot have 18 as their HCF and 380 as their LCM

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