Question

find the LCM and HCF of the pairs od integers using fundamental theorm of arithmetic and verify that LCM × HCF = product lf the two numbers 192 and 2880​

Answer 1

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☞ LCM = 2880

☞ HCF = 192

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$\huge\sf\blue{Given}$

✭ The Numbers 192 and 2880

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◈ Their HCF and LCM

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➝ 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3 = 2⁶ × 3

➝ 2880 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 3 × 3 = 2⁶ × 5 × 3²

LCM of 2 Numbers is given by the product of the largest power of all the factors,that is

➳ 2⁶ × 3² × 5

➳ LCM = 2880

HCF of 2 Numbers is the product of the least power of the common factors

»» 2⁶ × 3

»» HCF = 192

Verification

➠ LCM × HCF = Product of two Numbers

➠ 2880 × 192 = 192 × 2880

➠ LHS = RHS

$\sf Hence \ Proved!!$

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