Question

if two positive integer p and q are written as p=a2 b3 and q = a2 b;a,b prime number, then find LCM (q,p)​

Answer 1

Hey Mate!!

P=a²b³

P=a²b³q=a³b

P=a²b³q=a³bHCF (p,q) =a²b

P=a²b³q=a³bHCF (p,q) =a²bLCM (p.q)=a³b³

P=a²b³q=a³bHCF (p,q) =a²bLCM (p.q)=a³b³As we know that HCF(p,q)xLCM(p,q)=a²bxa³b³

P=a²b³q=a³bHCF (p,q) =a²bLCM (p.q)=a³b³As we know that HCF(p,q)xLCM(p,q)=a²bxa³b³=a⁵b⁴ ---------- equation 1

P=a²b³q=a³bHCF (p,q) =a²bLCM (p.q)=a³b³As we know that HCF(p,q)xLCM(p,q)=a²bxa³b³=a⁵b⁴ ---------- equation 1pq=a²b³xa³b

P=a²b³q=a³bHCF (p,q) =a²bLCM (p.q)=a³b³As we know that HCF(p,q)xLCM(p,q)=a²bxa³b³=a⁵b⁴ ---------- equation 1pq=a²b³xa³b=a⁵b⁴-----------equation 2

P=a²b³q=a³bHCF (p,q) =a²bLCM (p.q)=a³b³As we know that HCF(p,q)xLCM(p,q)=a²bxa³b³=a⁵b⁴ ---------- equation 1pq=a²b³xa³b=a⁵b⁴-----------equation 2from 1 and 2

P=a²b³q=a³bHCF (p,q) =a²bLCM (p.q)=a³b³As we know that HCF(p,q)xLCM(p,q)=a²bxa³b³=a⁵b⁴ ---------- equation 1pq=a²b³xa³b=a⁵b⁴-----------equation 2from 1 and 2we can say that HCF(p,q)xLCM(p,q)=pq