Question

is the product of three numbers always equal to the product of their hcf and lcm?

Answer 1

no the product of three numbers will never equal to the product of their hcf and lcm.

Answer 2

Answer

No, the product of any three numbers is not always equal to the products of their HCF and LCM.

Explanation

• The product of three numbers can be equal to the product of their HCF and LCM only when the numbers are prime numbers.
• The prime numbers are those numbers which can be divisible by 1 and itself.
• Their products may or may not be equal to their HCF and LCM if the numbers are not prime.
• For example, the first three prime numbers are 2, 3 and 5. The product =2*3*5 and the LCM=2*3*5*1 also HCF=1.
• Hence it is clear that for prime numbers their product is equal to the product of their HCF and LCM.
• Now take examples of other numbers which are not prime such as 4, 12, 6. The product = 4*12*6. The HCF=2 and LCM = 2*2*2*3*3.
• Hence it is clear that their product is not equal to the product of their HCF and LCM.

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