Question

find HCF and LCM of 540 and 72 .verify that HCF ×LCM = product of two numbers​

Answer 1

Given:

Two numbers are: 540 and 72

To find:

(i) H.C.F. and L.C.M

(ii) Verify that H.C.F. × L.C.M. = product of two numbers

Solution:

(i) Finding H.C.F and L.C.M:

By using the prime factorisation method, we will write the factors of 540 and 72.

540 = 2 × 2 × 3 × 3 × 3 × 5

72 = 2 × 2 × 2 × 3 × 3

Therefore,

H.C.F. (540 & 72) = 2 × 2 × 3 × 3 = 36

and

L.C.M. (540 & 72) = 2 × 2 × 2 × 3 × 3 × 3 × 5 = 1080

Thus, $\boxed{\bold{H.C.F. = 36}} \:and \:\boxed{\bold{L.C.M. = 1080}}$.

(ii) Verifying H.C.F. × L.C.M. = product of two numbers:

L.H.S.

= H.C.F. × L.C.M.

= 36 × 1080

= 38880

R.H.S.

= product of two numbers

= 540 × 72

= 38880

Thus, $\boxed{\bold{L.H.S. = R.H.S.}}$.

Hence verified

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