alleryFor the numbers 6, 72 and 120, which pair gives the HCF and LCM respectively?
A$6$ and $360$
B$12$ and $720$
C$6$ and $720$
D$3$ and $360$
Answer & Solution
Correct answer: A. $6$ and $360$
Their prime factorizations are $6=2\times 3$, $72=2^3\times 3^2$, and $120=2^3\times 3\times 5$.
The HCF uses the smallest common powers of common primes: $2^1\times 3^1=6$.
The LCM uses the greatest powers of all primes involved: $2^3\times 3^2\times 5=360$.
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