Find the positive integer a for which gcda84 12 and lcma84

Find the positive integer a for which gcd(a,84) = 12 and lcm(a,84) = 420

Solution

In the given question GCD is greatest common factor and LCM is least common factor.
And According to rule Product of GCD and LCM is equal to product of given two number of which LCM and GCD is to be found.
Means
GCD*LCM = a*84
given GCD =12 ,   LCM = 420

So,

12*420 = a * 84

a = 5040/84

a = 60             which is required answer..