Question

Lcm of two numbers is 14 time's their had.the sum of com and hcf is 600.if one number is 280 find the other

Answer 1

$\large{\boxed{\bold {Answer:}}}$

Let the HCF be x,

So the LCM will be 14X,

Sum of LCM and HCF = 600

$x + 14x = 600 \\ \\ = > 15x = 600 \\ \\ = > x = \frac{600}{15} \\ \\ = > x = 40 \\ \\ = > LCM = 14 \times 40 = 560$

Now,

$HCF \times LCM = X \times y \\ \\ = > 40 \times 560 = 280 \times y \\ \\ = > y = 40 \times \frac{560}{280} \\ \\ = > y = 80$

Hence, the other number is 80

$\large{\boxed{\bold {Hope\:it\:helps\:you!}}}$

Answer 2

GIVEN: HCF+LCM= 600, ONE NUMBER= 280

Let the HCF= X

LCM= 14X

HCF+LCM= 600

X+ 14X=600

15X= 600

X= 600/15

X= 40

HCF= 40

LCM = 14X= 14× 40= 560

HCF×LCM= 1ST NUMBER × 2ND NUMBER

40× 560= 280× 2ND NUMBER

2ND NUMBER= (40×560) /280

2ND NUMBER= 40×2

2ND NUMBER= 80