Find two numbers if their LCM is 120 & their HCF is 4.

LCM of the two numbers is 120. HCF of them is 4. To
find such numbers.

We know that if P and Q are the numbers
whose HCF is H, and LCM is M , then as H is the HCF, H should divide both Pand
Q.

P = H*p,

Q =
H*q.

where pq are integers prime to each
other.

Therefore H*pq = LCM =
120

pq = 120/4 = 120/4 =
30.

Now find pq such that pq = 30 and p and are prime to
each other.

30 = 30*1. Threfore P = 1*4= 120 and Q = 30*4 =
120.

30 = 2*15. Therefore P = 2*4 = 8 and Q = 15*4 = 
60

30 = 3*10. Therefore P= 3*4 = 12 and Q = 30*4 =
40.

30 = 5*6. P = 5*4 = 20 and Q = 6*4 =
24.

Therefore the following pairs have the HCF 4 and LCM =
120.

(20, 24), (12,40), (8,60) ,
(4,120).