Question

Can two positive numbers have 812 and 28 as their HCF and LCM respectively? How?

Answer 1

To check whether 812 and 28 are HCF and LCM of two positive integers, first check that Is LCM is a factor of HCF or not ?

If LCM is a factor HCF, then it is possible.

Let's check –

812 = 28 × 29

From this, we can conclude that LCM is a factor of HCF.

Hence,

Yes, two +ve integers have 812 as HCF and 28 as LCM.

Answer 2

TO FIND

whether 812 and 28 are HCF and LCM of two positive integers, first check that Is LCM is a factor of HCF or not ?

GIVEN

THE HCF IS 812 ADN LCM IS 28

SOLUTION

If LCM is a factor HCF, then it is possible.

Let's check –

812/2 = 406;

406/2 = 203;

203/7 = 29;

29/29 = 1;

812 = 2×2×7×29

812 =28×29

From this, we can conclude that LCM is a factor of HCF.

Hence,

Yes, two +ve integers have 812 as HCF and 28 as LCM.

ANSWER

YES,  there are two integers which have

• HCF=812

• LCM=28