Question

HCF of the two numbers $=$
A) Product of numbers $+$ their LCM
B) Product of numbers $–$ their LCM
C) Product of numbers $ \times $ their LCM
D) Product of numbers $ \div $ their LCM

Answer 1

Hint:
We have to find the H.C.F (Highest Common Factor) of the two numbers given with the help of its L.C.M (Least Common Multiple) and the product of the two numbers. H.C.F of a co-prime number is always equal to 1 as there will be no common number as their divisor whereas L.C.M of co-prime numbers is always equal to the product of the two numbers.

Complete step by step solution:
We know that the Product of the numbers is always equal to the product of their L.C.M and H.C.F where L.C.M is the least common multiple and H.C.F is the highest common factor of the numbers.
The formula for the relation between L.C.M (Least Common Multiple) and H.C.F (Highest Common Factor) of two numbers is given as
L.C.M $ \times $ H.C.F $ = $ Product of two numbers
So, as we have to find the H.C.F we can write the above formula as,
H.C.F $=$ Product of two numbers $ \div $ L.C.M

Hence, the option (D) is correct.

Note:
H.C.F (Highest Common Factor) is the greatest number that divides each of the given integers completely. L.C.M (Least Common Multiple) is the smallest number which is a multiple of the given numbers. As H.C.F contains all the common factors of two numbers and L.C.M contains all the factors irrespective of common or uncommon so the two of them combined have all the factors common in double and non-common in single and thus product of two numbers is equal to product of their least common multiple and highest common divisor.