Can 2 number have 16 as their HCF and 380 as their LCM? give reason

1.	Can 2 number have 16 as their HCF and 380 as their LCM? give reason
Answer» Here HCF=16Let the numbers be a and b.We know that a and b both are divisible by HCF\xa0and LCM is divisible by a and b bothHence, LCM must be divisible by HCF i.e; 16Now 380=23{tex}\\times{/tex}16 + 12We get that 12 is the remainder while dividing 380 by 16, It means that 380 is not divisible by HCF 16Therefore\xa0two numbers cannot have 16 as their HCF and 380 as their LCM

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