Question

can two positive integers have 18 as theri Hcf and 380 as their Lcm . give resons. maths sum​

Answer 1

Answer:

There can't be two numbers whose HCF = 18 and LCM = 380.

Step-by-step explanation:

We must find,

Two numbers whose HCF = 18 and LCM = 380.

Now,

Let 'a' and 'b' be two whole number coprimes.

Coprimes are numbers that have no common factor except 1, or in simple words HCF (of Coprimes) = 1.

Let the numbers be 18a and 18b.

Now, you might ask why I took the number to be 18a and 18b, instead of just a and b.

This is because, remember I said 'a' and 'b' are coprimes,

So their HCF = 1

But when its 18a and 18b, 18 is the Highest Common Factor, so HCF = 18.

Now, we know that,

Product of number = HCF × LCM

18a × 18b = 18 × 380

18 × 18 × a × b = (18 × 380)

(18 × 18)ab = (18 × 380)

ab = (18 × 380)/(18 × 18)

ab = 380/18

ab = 190/9

Now,

we said that a and b were whole number,

we should know that,

Product of 2 whole numbers will never be equal to a rational number (fraction).

So,

There can't be two numbers whose HCF = 18 and LCM = 380.

Hope it helped and believing you understood it........All the best