Question

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

Answer 1

Hint: As we know that the product of two numbers can be given as product of their H.C.F and L.C.M, the product of two numbers and it’s H.C.F is given we only need to form the equation and to calculate one unknown rest all the values are given in the question, hence our answer will be obtained.

Complete step-by-step answer:
As per the given, The product of two numbers is 2925 and their H.C.F is 15.
So, the product of two numbers can be given as,
Product of numbers \[ = \]H.C.F \[ \times \]L.C.M
Hence, putting the values in the above equation we get,
\[ \Rightarrow 2925 = 15 \times \left( {L.C.M} \right)\]
On simplification we get,
\[ \Rightarrow \]\[L.C.M = \dfrac{{2925}}{{15}}\]
On dividing we get,
\[ \Rightarrow \]\[L.C.M = 195\]
Hence, the LCM of the given two numbers is \[L.C.M = 195\].

Note:1.The product of the HCF and LCM of two numbers is equal to the product of the two numbers.
2.This case is only possible for two numbers, the product of 3 numbers is not equal to the product of their HCF and LCM.
3.The H.C.F. defines the greatest factor present in between given two or more numbers, whereas L.C.M. defines the least number which is exactly divisible by two or more numbers.