Question

The product of two numbers is 2925 and their H.C.F. is 15. Find their L.C.M.

Answer 1

Hint: We will use the formula: ${\text{(LCM}} \times {\text{HCF) of two numbers = product of those two numbers}}$ to solve this question for the value of LCM of those numbers whose product is given as 2925 and HCF as 15.

Complete step-by-step answer:
We are given that the product of two numbers is 2925.
The HCF of those two numbers is 15.
We are required to calculate their LCM.
We know that there is a property that: The product of the least common multiple (LCM) and the highest common factor (HCF) of two natural numbers is equal to the product of those two numbers.
Therefore, we can write it as: ${\text{(LCM}} \times {\text{HCF) of two numbers = product of those two numbers}}$
$ \Rightarrow {\text{LCM}} \times 15 = 2925$
$ \Rightarrow {\text{LCM = }}\dfrac{{2925}}{{15}} = 195$
Therefore, the LCM of the numbers is 195.

Note: In this question, you may get confused in the selection of the formula to solve for LCM of the two numbers.
LCM is defined as the smallest possible natural number which is a multiple of two or more natural numbers. Or, the least common multiple is the smallest positive integer that is evenly divisible by the numbers whose LCM is required (two or more than two).
HCF is defined as the greatest natural number which divides each of the numbers selected to find the HCF of. Or, the highest common factor of two or more numbers is the highest (or greatest) number among all the common factors of those numbers.