Question

The product of LCM and HCF of two number is 150. If one of the numbers is 15, find the other number.​

Answer 1

Step-by-step explanation:

If two numbers HCF is 15 and LCM is 150 find what the number is?

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First, factor the HCF and LCM.

15=3⋅5

150=2⋅3⋅52

The LCM has a factor of 2 and an additional factor of 5. Therefore, exactly one of the numbers will have a factor of 2, and exactly 1 of the numbers will have an additional factor of 5.

There are 2 combinations that will do that. The factor of 2 and the additional factor of 5 could be in the same number, or the factor of 2 and the additional factor of 5 could be in different numbers.

Therefore, the 2 numbers could be:

3⋅5=15

and

3⋅5⋅2⋅5=150

Alternatively, the 2 numbers could be:

3⋅5⋅2=30

and

3⋅5⋅5=75

Answer 2

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we have,

• product of LCM and HCF of two numbers = 150
• one number is = 15

we know that,

product of LCM and HCF of two numbers = product of numbers

let another number be x

and

$\bold{15 \times x = 150 }\\ \\ \bold{\implies x = \frac{150}{15}} \\ \\ \bold{\implies x = 10} \: \: \:$

so, other number is 10