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

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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).

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