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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 1

NCERT Exemplar Class 10 Maths Exercise 1.2 Problem 8

Summary:

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

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