If two positive integers m and n are expressible in the form m-a2 b3 and n-a3 b2- where a- b are prime numbers- then HCFm- n- and LCMa- b-

It is given that, nbsp;m nbsp;= nbsp;a2b3 nbsp;and nbsp;n nbsp;= nbsp;a3b2, where nbsp;a, b nbsp;are prime numbers. HCF (m, n) = nbsp;HCF ( ...

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Byju's Answer

Standard X

Mathematics

Method of Finding HCF

If two positi...

Question

If two positive integers m and n are expressible in the form m = a² b³ and n = a³b², where a, b are prime numbers, then HCF (m, n) = _ and LCM (a, b) = _.

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Solution

It is given that, m = a²b³ and n = a³b², where a, b are prime numbers.

HCF (m, n) = HCF (a²b³, a³b²)
= The lowest of indices of a and b
= a²b²

Hence, HCF (m, n) is a²b².

LCM (m, n) = LCM (a² b³, a³b²)
= The lowest of indices of a and b
= a³b³

Hence, LCM (m, n) is a³b³.

Hence, HCF (m, n) = a²b² and LCM (m, n) = a³b³.

Disclaimer: In the question, we need to find LCM (m, n) instead of LCM (a, b).

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