Question

The LCM of two numbers is 14 times their HCF . The sum of LCM and HCF is 600 if one number is 280, then find the other number.​

Answer 1

Answer:

Step-by-step explanation

LCM=14HCF

LCM+HCF=600

14HCF+HCF=600

15HCF=600

HCF=600/15

HCF=40

LCM=14HCF=14×40=560

Product of two given numbers= HCF×LCM

280×x=40×560

x=40×560/280

x=80

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Answer 2

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given That LCM of two numbers is 14 times their HCF
• The sum of LCM and HCF is 600
• One number is 280

To Find:

• We have to find both the numbers

Solution:

Let the HCF of the numbers = x

LCM of the numbers = 14x

____________________________

$\underline{\large{\red{\mathfrak{According\:to\:the\:Question :}}}}$

The Sum of LCM and HCF is 600

$\hookrightarrow \boxed{\sf{LCM + HCF = 600}}$

$\hookrightarrow \sf{ x + 14x = 600}$

$\hookrightarrow \sf{ 15x = 600 }$

$\hookrightarrow \sf{ x = \dfrac{600}{15}}$

$\hookrightarrow \sf{ x = 40}$

Therefore:

The HCF of numbers = 40

The LCM of numbers = 14 $\times$ 40 = 560

________________________________

Since we know that

Let the other number = A

$\implies \boxed{\sf{LCM \times HCF = Product\:of\:Two\:Numbers}}$

$\implies \sf{560 \times 40 = 280 \times A }$

$\implies \sf{22400 = 280 \times A }$

$\implies \sf{ A = \dfrac{22400}{280}}$

$\implies \sf{A = 80}$

Hence $\boxed{\red{\sf{Second \:Number = 80}} }$