Can two numbers have 24as their HCF and 480 as their LCM?? Give reasons
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Answer:Hi,
Let us consider, P and Q are the numbers whose HCF is H, and LCM is M , then as H is the HCF, H should divide both P and Q.
P = H*p,
Q = H*q.
where pq are integers prime to each other.
Therefore H*pq = LCM.
Given, HCF=24, LCM = 480
H*pq = LCM
or, 24*(pq) = 480
or, pq = 20
As, pq are integers prime to each other, thus p.q can only be 4,5
P = 24*4 = 96
Q = 24*5 = 120
Ans. 96 and 120 have their HCF 24 and LCM 480
Step-by-step explanation:Please mark as brainliest
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