Find the HCF of 96 and 404 by prime factorisation method amd hence find their LCM.
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Find the HCF of 96 and 404 by prime factorisation method amd hence find their LCM.
Find the HCF of 96 and 404 by prime factorisation method amd hence find their LCM.
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let a = 494 ; b = 96
Expressing the number as a product of prime number
404=2×2×101
96=2×2×2×2×2×3
∴ LCM of 404 and 96 is 2×2×2×2×2×101×3=9696
∴ HCF of 404 =2×2×10196=2×2×2×2×2×3
∴ LCM of 404 and 96 is 2×2×2×2×2×101×3=9696
∴ HCF of 404 and 96 is 2×2=4Now HCF×LCM=4×9696=38784
Product of two given numbers 404×96=38784
Hence HCM×LCM= product of two given numbers.
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Verified answer
[tex]\huge\star{\underline{\mathtt{\red{A}\pink{n}\green{s}\blue{w}\purple{e}\orange{r}}}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf\pink{96=2×2×2×2×2×3={2}^{5}\times{3}^{1}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf\red{404=2×2×101={2}^{2}\times{101}^{1}}[/tex]
[tex]\Large\sf\underline\green{Therefore,}[/tex]
[tex]\longrightarrow[/tex][tex]\sf\purple{HCF\:=\:2\:×2\:=\:4}[/tex]
[tex]\Large\sf\underline\orange{Also,}[/tex]
[tex]\longrightarrow[/tex][tex]\sf\blue{HCF\:×\:LCM\:=\:product\:of\:2\:numbers}[/tex]
[tex]\longrightarrow[/tex][tex]\sf\orange{4\:×\:LCM\:=\:96\:×\:404}[/tex]
[tex]\longrightarrow[/tex][tex]\sf\pink{LCM= \frac{96 \times 404}{4}} [/tex]
[tex]\longrightarrow[/tex][tex]\sf\red{LCM\:=\:96\:×\:101}[/tex]
[tex]\longrightarrow[/tex][tex]\large\sf\green{LCM\:=\:9696}[/tex]