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Highest common factor of three distinct numbers is 7 and their least common multiple is 42. If all numbers are less than the least common multiple, then what is the product of these three numbers?

Highest common factor of three distinct numbers is 7 and their least common multiple is 42. If all numbers are less than the least common multiple, then what is the product of these three numbers? Correct Answer 2058

Given:

The LCM of three numbers = 42

The HCF of three numbers = 7

Concept:

HCF is the highest common factor of some given numbers. When we divide the numbers by their HCF, the quotients will be prime to each other.

LCM = HCF × Product of the quotients after dividing the numbers by the HCF

Calculation:

⇒ The possible number is 7, 14, 21, and 42 where 42 can not fulfil the condition because number should be less than 42

⇒ So, the number is 7, 14, and 21

⇒ The product of these number  = 7 × 14 × 21 = 2058

∴ The required result will be 2058.

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The formula LCM × HCF = Product of the numbers is only applicable in the case of two numbers.

When it comes to three or more numbers it will not work.

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