Question

1. If HCF of two numbers is 12 and their product is 360, then their LCM is (a) 60 (b)40 (c) 30 (d) None of these
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Answer 1

30

Step-by-step explanation:

HCF of two numbers= 12

Their product = 360

LCM= Product of two nos

HCF

= 360

12

= 30

Answer 2

Given:

If the HCF of two numbers is 12 and their product is 360, then their LCM is?

To find:

Their L.C.M.

Solution:

If a and b are the two numbers then the relation between their L.C.M. and H.C.F. is as follows:

$\boxed{\bold{H.C.F. \times L.C.M. = Product\:of\:two \:given \:numbers = a\times b}}$

Here we have,

H.C.F. of the two numbers = H.C.F. (a and b) = 12

The product of the two numbers = a × b = 360

Now, on substituting the given values into the above relation of HCF and LCM, we get

$12 \times L.C.M. = 360$

$\implies L.C.M. = \frac{360}{12}$

$\implies \bold{L.C.M. = 30}$ ← option (c)

Thus, the L.C.M. of the two numbers is → 30.

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