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