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The ratio of least common multiple and highest common factor of 16 and 36 is
Question



The ratio of least common multiple and highest common factor of 16 and 36 is

A.

36:1

B.

16:1

C.

1:36

D.

72:1

Correct option is A

Solution:Given numbers: 16 and 36Prime factorization:16=2436=22×32LCM (Least Common Multiple): Take the highest powers of all primesLCM=24×32=16×9=144HCF (Highest Common Factor): Take the lowest powers of common primesHCF=22=4Ratio of LCM to HCF:LCMHCF=1444=36:1The correct answer is: (a) 36:1\textbf{Solution:} \\[5pt]\text{Given numbers: } 16 \text{ and } 36 \\[5pt]\text{Prime factorization:} \\16 = 2^4 \\36 = 2^2 \times 3^2 \\[5pt]\text{LCM (Least Common Multiple): Take the highest powers of all primes} \\\text{LCM} = 2^4 \times 3^2 = 16 \times 9 = 144 \\[5pt]\text{HCF (Highest Common Factor): Take the lowest powers of common primes} \\\text{HCF} = 2^2 = 4 \\[5pt]\text{Ratio of LCM to HCF:} \\\frac{\text{LCM}}{\text{HCF}} = \frac{144}{4} = 36:1 \\[10pt]\boxed{\text{The correct answer is: (a) } 36:1}​​

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