Question

Two positive integers are in the ratio of 3 : 4. their HCF and LCM are in the ratio of 1:12. If the difference between their LCM and their HCF is 44 then wha the sum of the numbers?​

Answer 1

Answer:

Here your answer is:-

Step-by-step explanation:

Let the number be 3x and 4x

LCM*HCF=product of two numbers

4*LCM=3x*4x

LCM=12x²/4

LCM=3x²

LCM of 3x and 4x=12x

12x=3x²

x=4

LCM=48

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Answer 2

Answer:

28

Step-by-step explanation:

let,the two positive integers be 3x and 4x.

Acc. to the question,

h.c.f.:l.c.m.=1:12

so,l.c.m.= 12 h.c.f.

according to the question,

L.C.M. - H.C.F. = 44

=> 12H.C.F. - H.C.F.= 44

=>H.C.F.=4

we know,

h.c.f. × l.c.m. = product of two numbers

=> 12 h.c.f × h.c.f. = 3x × 4x

=>h.c.f.= x

so,h.c.f=x=4

now,the two positive integers are 3×4 i.e.12 and 4×4 i.e. 16

sum= 12+16= 28.