Question

The HCF of 60 and 72 is 12. Find their LCM.

Answer 1

Hint: We have to proceed by writing each number as a product of its prime factors and then we know that the lowest common multiple is found by multiplying all the factors which appear in either list of the prime factors of both the numbers.

Complete step-by-step answer:
Given numbers 60 and 72
HCF of these two numbers is 12
To find LCM of these two numbers, first find the prime factors of 60 and 72,
Factors which are prime i.e it can be only divided by 1 and by itself are said to be Prime factors.
Prime factors of 60$ \to 2 \times 2 \times 3 \times 5$
Prime factors of 72$ \to 2 \times 2 \times 2 \times 3 \times 3$
We know that the highest common factor is found by multiplying all the factors which appear in both lists. Similarly the lowest common multiple is found by multiplying all the factors which appear in either list.
$LCM{\text{ of 60 and 72 }} \to {\text{ 2}} \times {\text{2}} \times 2 \times {\text{3}} \times 3 \times 5 = 360$

Note: While finding LCM we have to remember to multiply the prime factors only once whose pair is made in both lists , it does not mean that they should be multiplied only once while calculating LCM , it means that if they are part of the pair then we only have to multiply one from the pair , if the prime factor does not make any pair we need to multiply it separately to get to the desired answer. Note that the product of LCM and HCF is equal to the product of those two numbers therefore this question could also be solved by substituting HCF and the two numbers in the equation, LCM HCF = Product of two numbers.