Question

if the two numbers are in the ratio of 2:3 and the product of their highest common factor and least common multiple is 150 find the sum of the number​

Answer 1

let the numbers be 2x and 3x

Product of HCF and LCM = Product of the numbers

$lcm \times hcf = \: n1 \times n2$

LCM×HCF=150

n1×n2=150

2x×3x=6x^2=150

x^2=25

x=5

$\sqrt{25}$

Answer 2

The sum of the number is 25.

Step-by-step explanation:

Since we have given that

product of HCF and LCM = 150

Ratio of number =  2 : 3

So, the first no. = 2x

Second number = 3x

According to question, it becomes,

$HCF\times LCM=a\times b\\\\150=2x\times 3x\\\\150=6x^2\\\\\dfrac{150}{6}=x^2\\\\25=x^2\\\\x=5$

Hence, the sum of the number is 5x =5×5 = 25

# learn more:

The least common multiple of two numbers is 24. The sum of the two numbers is 20.

What are the numbers?

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